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Home , Partha Ghose, Satyendra Nath Bose

Purnangshu Kumar Roy and the S.N. Tradition in Theoretical By Charles Wesley Ervin Email: [email protected] August, 2016

INTRODUCTION This year Calcutta University marks a historic mile- stone. One hundred years ago the university started teaching physics courses at the newly created College of Science and Technology. Three of the most brilliant Indian of the twentieth century began their careers there. C.V. Raman, the first Palit Professor of Physics, was awarded the Nobel Prize in 1930 for his work on scattering. The two young lecturers, and , made major breakthroughs even sooner – Saha in 1920 for deriving the equation that accounts for the spectral classifica- tion of stars and Bose in 1924 for inventing the statisti- cal model that validated Einstein’s hypothesis of light quanta (the Bose Statistics). But this “golden age” of Calcutta physics was P. K. Roy (right) with Satyendra Nath Bose in London, short-lived. Saha went to Allahabad University in March, 1958. Roy studied with Bose for 1923, Bose decamped to Dacca University in 1924, ten years at Calcutta University and then earned his PhD at and Raman left in 1932 to become the first Indian di- Imperial College under . This photo was taken when Bose came to London to be inducted Fellow of the rector of the Indian Institute of Science in Bangalore. Royal Society. Courtesy of Anjana Srivastava. After the war, however, there was something of a re- naissance. Bose returned in 1945 and gathered a team of talented research workers in the Physics Depart- ment and the Khaira Lab. In this article I focus on one of his outstanding protégés, Purnangshu Kumar Roy, who carried forward the tradition of the “golden years” of Calcutta physics. He studied – relativity, quan- tum , and – with his mentor Bose for ten years and then went to London in 1957 to do his PhD in at Imperial College under Abdus Salam, the future Nobel Laureate. Upon his return to Calcutta, he joined Bose’s team at the Indian Association for the Cultivation of Science and in 1964 became Senior Scientist and then Reader in Pure Physics at Calcutta University. Roy could have had a successful academic career abroad. But like Bose, Roy was a Calcutta man at heart - a true Bengali intellectual who pursued science, culture, and politics with equal zest and who loved nothing more than spending hours in freewheeling group conversations in the smoky coffee shops near the university. Though he didn’t publish much after 1962, he pursed the latest developments in particle physics and the ongoing search for a Unified Field Theory. Sadly, he died of cancer in 1975, when he was only 50. I met Dr. Roy in Calcutta in 1974. After that, we lost contact. When I heard about the plans of Calcutta University to celebrate the centenary of its Physics Department, I wrote a short biographical sketch of Dr. Roy for the commemoration volume.1 This expanded article places him in broader context. I express my gratitude to his daughter, Anjana Srivastava, in Mumbai and his nephew, Mukul Roy, in for provid- ing critical biographical information and his former colleagues and students for sharing their recollections. FAMILY BACKGROUND AND UPBRINGING P.K. Roy was born into a middle-class Bengali family with ancestral roots in Howrah, across the Hoogli River from Calcutta. His grandfather, Beni Madhab Roy, owned land there. They were Vaidyas in caste. The Vaidyas considered themselves to be of the same high caste as Brahmins. P.K. Roy’s father, Raj Kishore, was a college graduate who secured a good government job in the Defense Accounts Department. In 1908 he was transferred from Howrah to Meerut, an old town northwest of Delhi. His wife, Radha, bore him eight children – five sons and three daughters. Purnangshu was the youngest, born February 10, 1925. The sons were given names that referred to the Moon. Purnangshu is “full moon.” Raj Kishore was loyal to the Raj and he rose to a middle rank in the bureaucracy. He was very cultured. He wrote poetry, and the sound of often filled the home. His sons remember him as a patriarch and they always addressed him with the respectful “you” (apni), which was common in those days. He knew that education was the ticket to a good salaried job in the British administration and he sent the children to English-medium schools. But in the home, the traditional Bengali culture prevailed. Like many to this day Raj Kishore and Radha gave their children nicknames or petnames (dak nam). Purnangshu was “Nitai” - shortened from Nityananda, the 15th century Vaishnava saint who was an important religious fig- ure within the Gaudiya Vaishnava tradition of . For the rest of his life, Purnangshu went by “Nitai.” After retiring from government service in 1926, Raj Kishore decided to move the family back to Cal- cutta. He bought a plot of land in Nanda Kumar Chaudhuri Lane, a narrow street barely ten feet wide, tucked away behind the intersection of bustling Vivekananda Road and Cornwallis Street (now Bidhan Sarani). This was an old residential area of North Calcutta, populated by families whose wealth came from land their ancestors had acquired from the British as a result of the Permanent Settlement. With borrowed money he built a large, three-story house for the joint family. His wife died in childbirth before it was finished in 1928. He installed plaque on the front of the house with the dedication, Radha-Kun- ja [abode of Radha]. The plaque is intriguing. In those days devout Vaishnava families often put up plaques that referred to the god Krishna (Krishna Kunja - the abode of Lord Krishna). Dedications to the godess Radha were tradi- tionally suffixed by Krishna’s name, e.g., Radhamad- hav, Radhavinod, etc. “Radha” rarely stands alone. So “Radha-Kunja,” could refer to either the Vaishnava tradition or his wife, or perhaps both. Purnangshu grew up in this house, surrounded by his brothers and sisters, nieces and nephews, and domestic helpers. On the ground floor there were two large parlors, an interior courtyard with water tank, kitchen, and servants’ quarters. The elder brothers lived on the second floor. Purnangshu, being the youngest, had a small room on the top floor. At one point there were a total of 42 people living there. There was only The Roy residence, 13 Nanda Kumar Chaudhuri Lane, one bathroom for the entire household. There was no North Calcutta. The dedication plaque from 1928 is on the wall next to the entrance. Courtesy Anjana Srivastava. yard outside, so the children congregated on the stair- way. Despite the cramped quarters, they loved the house and being a tight-knit joint family.

Page 2 A WHIZ Roy was schooled at Scottish Church Collegiate School, one of the old- est English-medium educational institutions in . The school had top-quality teaching staff, a well-stocked library, and up-to-date labora- tory. Roy was precocious; his room was filled with books on all sorts of subjects. But he wasn’t a bookworm. He made many friends at school. A relative described him as “very sincere, outgoing, and easy going.”2 He excelled in mathematics. In 1942 he passed the Intermediate Science Examination (ISc) in the First Division with a star and dis- Roy graduated with top honors from Scottish Church College in North Cal- tinctions in Mathematics, the highest score in the College. He won two cutta, not far from the Roy residence. prizes in Mathematics and two scholarships. He continued in the BSc Photo: Calcutta University (Honors) program at Scottish Church College. His father died in 1941. The elder sons kept the family afloat with their incomes. But the future looked precarious. The war was getting closer every day. The Japanese had routed the British in Burma and were massing forces at the border in preparation for an invasion of Bengal. Their planes bombed the Calcutta docks. Families boarded up their houses and fled the city. In August, 1942 the Quit India struggle erupted after the British arrested Gandhi and the entire Con- gress high command for their refusal to support the war. Purnangshu and his sister, Suprova, who was an economics student, joined the mass demonstrations. They got a quick lesson in politics. The Communist Party of India was supporting the British war effort in the name of defending Soviet Russia. Purnangshu and Suprova encountered a small group of Trotskyists (followers of the Russian revolutionary, Leon Trotsky, who was assassinated in his Mexico exile by a Stalinist agent in 1940). They were a very brainy lot who attacked the CPI from the left. Purnangshu and his sister joined the Trotskyist group.3 In 1944 Roy passed his BSc Examination with honors in Mathematics, ranking first among the students at Scottish Church College. The Principal sang his praises: “He was one of the most brilliant students of his time in College, obtaining uniformly high marks in his class examinations.”4 He matriculated in the MSc program in Applied Mathematics. The courses were given at the University College of Science, which was a constituent of the Calcutta University.

FORMING A BOND WITH BOSE While pursuing his MSc, Roy met the famous , Satyendra Nath Bose, who had returned to Calcutta in 1945 from Dacca University to become the Khaira Professor of Theoretical Physics at the Science Col- lege. Roy revered him like a demi-god. His teachers in the Applied Mathematics Department went to Bose for help with difficult problems or guidance. His door was always open to anybody who cared to drop in. He did not believe in any formality. At his Calcutta home he received visi- tors in his bedroom, which also served as his study. People streamed in; he never refused an audience. No appointments were needed.5 Purnangshu became a frequent visitor. Bose recognized his brilliance and enjoyed his sparkle. They had much in common beyond the classroom: love for Indian music, great literature, freewheeling group conversations (what Benga- lis call an adda), and politics. Bose was sympathetic to the Soviet experiment, supported the Indian nationalist movement, including the armed struggle of the S.N. Bose in 1949. revolutionary nationalists, and greatly admired Nehru for his progressive ideas about scientific development of a free India (“dams and laboratories are the temples of modern India”).

Page 3 Bose treated Roy like a son, addressing him tui (the intimate “you” in Bengali). Roy would often hang out at the Bose residence in the Goabagan neighborhood of North Calcutta. He was on very friendly terms with the entire joint family there. Bose would likewise drop in at the Roy residence for chats in the ground floor parlor. This kind of close professor-student relationship was very rare in India in those days. In 1947 Roy passed the MSc exam in Applied Mathematics with flying colors, placing first in the Second Class in the university order of merit. He got a job teaching physics at Vidyasagar College. At that point Calcutta was going through the living nightmare of the Partition. Several million desperate Hindu refugees from Eastern Bengal poured into Calcutta. The city administration struggled to cope. The Nehru government, beset with one crisis after another, had few resources for dams and laboratories at that point. Theoretical physics was not a priority. Roy frequently visited S. N. Bose at his home in Ishwar Mill Lane. Source: S.N. Bose Archives. A LONG APPRENTICESHIP In 1948 Roy became a graduate student in the Physics Department at the Science College. He joined the mathematical physics group, which included his classmates from the Applied Math department, Mahadev Dutta and Jagadish Sharma, as well as students from the MSc program in physics.6 The experimental team in the Khaira Laboratory pursued diverse projects, ranging from analysis of Indian clay minerals to inno- vative measurements of photoluminescence.7 As is well known, Bose insisted that his research students practice swadeshi and build their own lab equipment, using local technicians and materials. The environment was almost Socratic. Roy and his classmates went to Bose’s office for their seminars. They all sat around a large In the early 1950s Bose’s team built table. Bose didn’t lecture, he narrated. an innovative spectrophotometer that He used to work out detailed and distinctly written out steps measured photoluminescence afterglow of calculations on sheets of paper with meticulous care when more precisely than existing devices. Photo: Calcutta University. he gave us courses …He would bring out, off and on, the beauty of the broader perspective of physics, as he talked on and on for hours to the students sitting around his table…We had discussions on topics covering a wide range in and beyond Science, of our common interest in music, art, philosophic and social aspects of science. He would often get involved in stories of ordinary human life flowing with wit, humor and compassion.8 In most physics departments a brilliant student like Roy would have been put on a fast track to get a doctorate. But Bose had his own priorities. He seemed to care the least about the publication of scientific papers, which any other sci- entist would have thought to be the most important object, if not the only objective of his life. It is useful to remember that Bose did not submit a doctoral thesis on his own and did not think much of a doctorate degree. To many of his students doing research under him this may have seemed like an enigma. To them the submission of a doctoral thesis was a matter of professional survival, but they received no encouragement from their guide who thought knowledge was much more important than getting a doctorate degree.9 These unorthodox values of Bose had their pros and cons. On the one hand, Roy got a broad and deep

Page 4 foundation in physics from Bose before he had to specialize. Bose didn’t think much of textbooks. He had Roy work his way through the original papers and books on , Relativity, and Mechanics. Roy had to master differential equations, tensor calculus, calculus, complex integration, and matrix mathematics. On the other hand, Roy spent his prime years in apprenticeship, while his contemporaries elsewhere had already gotten their PhDs In 1954 Roy met (left), the and were churning out the research papers that were required to architect of Quantum Electrodynamics, establish a reputation in the physics community. One of Roy’s star when he visited Bose (right) in Calcutta. students in the sixties, Dipanjan Rai Chaudhuri, laments: Dirac spent time in informal discussions with Roy and other students. The ten years in tutelage to Bose may well be taken as Source: Meghnad Saha Archives. wasted years. While was learning to gauge gravity, P.K. Roy was cobbling with luminescence! Bose might have been teaching his stu- dents ‘research is research is research,’ but what was so revolutionary in restricting the future particle physicist [Roy], whom the gods loved, to chemical physics?”10 Another grad student of that era, the late Amar Kumar Raychaudhuri (no relation to Dipanjan), recount- ed in his memoirs how he got very little encouragement or help from either Saha or Bose.11 He eventually withdrew and, working on his own, made a fundamental contribution to relativistic cosmology.

“YOU GO TO ABDUS” In 1956 Bose was offered the position of Vice-Chancellor at Visva-Bhartati, the liberal arts university that had founded in rural Santiniketan in 1921. Bose accepted. He urged Roy to pursue a doctorate forthwith. He recommended Imperial College of Science and Technology in London. Traditionally an engineering school, Imperial wanted to develop a cutting-edge program in particle physics within the Applied Mathematics Department. They recruited a rising star from Cambridge, Abdus Salam, Abdus Salam at Cambridge along with his close collaborator, Paul Matthews, who had been one of his University at age 21 (1947). PhD advisors. One year younger than Roy, Salam had solved one of the Photo: Library, most difficult problems in Quantum Electrodynamics – renormalization of International Centre for Theo- “overlapping infinities” – before he finished his PhD dissertation in 1951.12 retical Physics, Trieste. As the story goes, Bose said to Roy, “Ja tui Abdus er kache ja” [You go to Abdus]. Roy duly applied to Imperial and was accepted into the new PhD program in the De- partment of Mathematical Physics. Fortuitously, his brother, Sitangshu, was then living in London, very close to Imperial College, and the two shared the flat. Another brother, Himangshu, a successful cardiologist in Calcutta, provided financial support.

“A VERY EXCITING PLACE TO BE” In October, 1957 Roy matriculated at Imperial College. The Applied Queensbourough Terrace, London. Mathematics Department was situated in the Huxley Building on Exhi- Roy and his brother lived in the bition Road in South Kensington, built in 1864 for the School of Naval last house on the left. Architecture and later home for the Royal School of Science.

Page 5 The department had just three staff - Salam, Matthews, and a young lecturer, John C. Taylor. There were only about twelve PhD students. They all sat in a common room, where they worked, conversed, ate lunch, and took their tea. Roy was in the Physics Group. His team- mates included Ray Streater and Tom Kibble from the UK, Erasmo Mad- ureira Ferreira from Brazil, Claud Lovelace from South Africa, Riazuddin from Pakistan, and fellow Bengalis, Ashok Kumar Gupta, D.K. Guha, and Muhammad Munirul Islam.13 Roy was the consummate team player. Fer- reira remembers him as being very friendly.14 In his memoirs Ray Streater recounted how Roy introduced him to Arthur Wightman’s work on axiom- The Mathematics Department was atic physics.15 then housed in the old Huxley Building, now the Henry Cole In those days particle physics was a wild ride for professors and stu- Wing of the V&A Museum. dents alike. Once upon a time (twenty or so years ear- lier) physicists thought nature was comprised of just FIGURE 1. The In nities in Quantum States three elementary particles – proton, neutron, and elec- A. Constant generation of the cloud tron. But rapid advances in particle acceleration and collision detection technologies after the war enabled γ experimentalists to lift the veil on the subatomic world e- little by little. New and unexpected particles, some Moving electrons (e) constantly emit and absorb (γ). Given the infi nitesimally short time (10-24 with baffling properties, were detected one after an- seconds) involved, the energy (E) of the superposed other: muons, pions, the neutrino, kaons, the lambda, states becomes indeterminately large, according to the sigma, and xi , and the delta particle. The Uncertainty Relation ΔEΔt ≤ ħ/2. theoretical physicists struggled to determine the basic B. Anti-particle whirlpools within the cloud quantum properties of these particles - their , an- e’+ gular , and parity.16 γ e‘- γ To make matters even more challenging, some of e- these particles seemed not to obey certain fundamental Photons can morph into electron-positron pairs (e– e+), laws. The Tau and Theta, for example, were produced adding further energy indeterminacy. in the same way and had identical properties, but their C. Endlessly nesting processes decay products had different parities. That seemed to violate the law of conservation of parity. Then the im- γ possible happened. In December, 1956 an experiment e- at Columbia University confirmed that parity isn’t As these virtual processes pile up, the superposed conserved in interactions occurring through the nucle- energy states become theoretically infi nite. ar “weak” force. The head of Columbia’s Physics De- In the 1930s physicists tried without success to calcu- partment expressed the shock that rippled through the late the energy of the electron in these processes. After international physics community: “A rather complete the war, new mathematical methods were devised to theoretical structure has been shattered at the base and circumvent most of the infi nities. But the overlapping infi nities remained problematic.12 we are not sure how the pieces will be put together.”17 When Roy arrived at Imperial College, Salam already had a plan to put the pieces together. In his first lecture he stated “how deeply privileged our generation is to have been presented with this fascinating challenge” and pledged to find the “stepping stones to an inner harmony, a deep pervading symmetry which we shall discover.”18 The “we” included Roy. He was promptly harnessed to the Salam-Matthews research chariot along with several other students in the Particle Physics Group.19 His classmate, Tom Kibble, remi- nisced, “It was a very exciting place to be, and a very exciting time in theoretical physics.”20

Page 6 THE SEARCH FOR DEEP SYMMETRY Roy was assigned to work on the K-mesons (kaons). Mesons are quasi-stable particles first detected in cos- mic rays in 1947. The kaons came in a triplet: the same particle with a positive charge (K+), negative charge (K–), and no charge (K0). They were , i.e., one of the family of particles that obey Bose Statistics, a subject that Roy knew very well.21 They had spin 0, but their parity wasn’t yet known. What was puzzling was that the kaons were produced by the nuclear “strong” force, which conserves parity, but decayed in a manner indicative of the weak force, which had just been proven not to conserve parity. For that reason the kaons were assigned a new , called “strangeness.” Salam and Matthews were very keen to resolve this mystery. It is tell- ing that they gave such an important assignment to Roy. Roy at Imperial College. He was known for his good sense of humor. A team in Europe had just published results of an experiment in Courtesy Anjana Srivastava. which a beam of negative kaons (K–-mesons) was directed at liquid Hydrogen-2, an atom with a two-nucleon nucleus.22 The collisions produced a fireworks of short-lived “strange” particles, the Sigma (Σ) and the Lambda (Λ), which were hyperons with unknown parities. But their isospin and angular momenta were properties that are conserved in nuclear reactions.23 Roy thus set out to use isospin and angular momentum as his stepping stones. In so doing, he was pioneering a method of analysis that would later become widely used. Strangeness and isospin constituted new and empirically useful analytical tools with which to make sense of the properties of the many new particles discovered in the 1950s. Isospin, moreover, brought economy as well as order by grouping different particles into multiplets. As far as the strong interactions are concerned, theorists had effectively fewer particles to deal with, since they had only to consider the overall properties of the multiplets rather than the individual members of each. In the latter half of the 1950s many theorists attempted to build on this success, looking for ways to achieve even greater economy by grouping par- ticles into larger families...In theoretical physics there is a direct connection between con- served quantities and ‘symmetries’ of the underlying interaction. Thus the , which conserves isospin, is said to possess an isospin symmetry.24

DISPERSION RELATIONS The mathematical tools that Roy used were called dispersion relations. In a nutshell, dispersion relations are sets of equations that relate input and output in particle scattering (dispersion) experiments. Salam and Matthews had already made significant contributions to developing the complex foundational mathematical theory.25 But working out the dispersion equations for each type of particle interaction was demanding and time-consuming work. That work was delegated to Roy. Roy had to derive sets of complex linear differential equations that defined every possible transition state in the reaction. His mathematical exercise culminated in a set of selection rules, which give the angular distribution of the hyperons (the Σ and Λ particles) that would correspond to an even parity K-meson versus an odd parity K-meson. The either-or rules can’t predict parity; they can only tell the experimentalist what to look for.26 As Roy concluded, “These rules may then distinguish, through the energy dependence and angular distribution, between a scalar [even parity] and a pseudoscalar [odd parity] K–-meson…by careful observations on the present experiments.” In late 1958 his paper was published in the journal, Nuclear Physics, a significant achievement for a first-year PhD student.27 The field of dispersion relations was evolving so fast that his work was soon outdated. Six months later a research team at Duke University reported an experiment that suggested the K–- meson had odd (-1) parity.28 But it took four more years of experiments to finally resolve the question: K-mesons are spin-0

Page 7 particles with odd parity; Σ and Λ are spin ½ particles with even parity.29 And the reason why these parti- cles had to have those parities became clear only with the development of the quark model for the hadrons nearly ten years later. In hindsight, what is notable about Roy’s paper is the focus on isospin. After it was published, others picked up the approach.30 Isospin proved to be the right stepping-stone. It led physicists in the early 1960s to investigate the symmetry models of group theory – SU(3) and SU(6) – which in turn were the stepping stones to the Eightfold Way classification scheme, the quark thesis, and eventually the .

SECOND PAPER At that point the theory of dispersion relations was limited to simple, “elastic” scatterings, where two particles, such as a π-meson and proton, ricochet off each other intact. Depending on the energies of the particles, the collision can excite the proton to a higher energy state, called a “resonance.” Dispersion theory predicted that the excited proton would have total angular momentum J = 3/2 and isospin S = 3/2. When pion-nucleon scattering experiments confirmed this prediction, the proponents of dispersion relations pos- ited that this 3/2, 3/2 resonance (“3, 3” in shorthand) would dominate the scattering process even at higher energies. Salam and Matthews asked Roy to investigate this assumption for high-energy K-meson-nucleon scat- tering. Roy derived dispersion relations for the two most likely angular momentum states, called the P-state and D-state, which correspond to angular momentum 0 and angular momentum 1, respectively. The as- sumption was that the P-state would dominate. On the basis of his analysis Roy concluded, “The dispersion relations give no grounds to expect any resonance in the P states in spite of the similar space properties of π and K mesons.” On the contrary, “the K-N [K-meson-nucleon] scattering should be dominated by the S-waves over a considerable range.” His conclusion was bolstered by the experimental data: the K-meson scattering was dominated by S-waves for lab beam energies of up to 200 MeV.31 His paper was published in Physical Review Letters.32 Salam and Matthews cited it in their next co-au- thored article on particle scattering.33

ONSET OF A DEBILITATING DISEASE During this period, Roy started to suffer pain and stiffness in his lower back. He went for an exam and was diagnosed with ankylosing spondylitis, a chronic rheumatic disease that causes inflammation and progres- sive degeneration of the spine and sacroiliac joints. There is no cure. Since the 1930s British doctors had been prescribing doses of therapy – x-rays and injections of radium – to help reduce the pain. Roy began to receive doses of radiation.

PhD THESIS In October, 1959 Roy submitted his PhD thesis, titled “Some Topics in Elementary Particle Physics.”34 The thesis basically was his first two research papers bracketed together. He updated the first paper with data from recent experiments in Europe that reinforced his assumptions about K-meson capture by a two-nucle- on system. He greatly expanded the second paper and drew more decisive conclusions: Thus the main and significant conclusion of the present work is that the dispersion theoretic analysis, in the ‘truncated’ form, of non-forward scattering is capable of discriminating be- tween a scalar and pseudoscalar K-meson on qualitative grounds alone. The results strongly indicate that the K-mesons are pseudoscalar.35 After submitting the thesis, Purnangshu left for home. His PhD was formally conferred on February 17, 1960.

Page 8 THE INDIAN ASSOCIATION FOR THE CULTIVATION OF SCIENCE Back home, Roy re-connected with Bose, who had recently returned to Calcutta after two years at Vish- wa-Bharati. Bose wanted to “make an intensive study of theoretical developments in nuclear physics in order to obtain greater insight into the nature of the fundamental particles and the laws of interaction.”36 He was an Emeritus Professor at both Calcutta University and the Indian Association for the Cultivation of Sci- ence (IACS), located in Jadavpur, South Calcutta. Bose was also named a “National Professor,” the highest academic honor the Indian government can bestow on an academic. The IACS offered better resources than the Science College at Calcutta University. Bose invited Roy to join his new team at IACS as the Senior Research Officer attached to the National Professor of Physics. Bose got a government grant that enabled Roy to pursue his research in fundamental particle physics. In 1960 Roy published another paper on relativistic dispersion relations for K-mesons in Nuclear Phys- ics.37 This paper was an amplification of some topics in his thesis. In early 1961 the National Institute of Sciences of India invited him to speak on Relativistic Dispersion Relations at a Particle Physics Sympo- sium. In his presentation Roy showed his command of the subject, discussing the strengths and weaknesses of the different approaches to particle scattering: the S-matrix school of Geoffrey Chew, the double disper- sion hypothesis of Stanley Mandelstam, and Regge theory.38

FACULTY POSITION AT CALCUTTA UNIVERSITY In 1964 Roy was offered the position of Senior Scientist in the Department of Pure Physics at Calcutta University. He had a heavy workload: teaching the MSc course in , delivering seminars and colloquia, and guiding PhD students, such as Padmanabha Dasgupta and Salil Roy.39 Roy loved teaching and he wanted his students to have the same kind of engaging, inspiring experience that he had as a student of Bose. Lokenath Debnath, then a PhD student in the department, recounts, “I learned a lot of mathematics from him. He was a wonderful person and extremely helpful.” 40 Another grad student, Indrani Bose, recalls, “He was very much respected for his deep scholarship. He gave the students very interesting problems as homework assignments.”41 He was approachable and informal. He turned manners upside down by addressing his students with the respectful “you” (apni). Most students addressed him “Sir,” but his close circle of proteges used his nickname, “Nitai babu,” or even shortened it further to “Tai babu.” In the Kolkata of the sixties and seventies, many things were in the cauldron, but friendship on equal terms between a don and his pupils was yet to emerge. Purnangshu Roy achieved the impossible. I have been fortunate in my life. Three persons of the previous generation have given me that love without judgment about which our poet Tagore has written. “Sir” [Purnangshu] was one of them. Forty years have passed since he left us, but the wound is still fresh.42

STARTING A FAMILY LIFE In 1964, at age 39, Roy married. That was a late age for marriage in those days. But the marriage was quite out of the ordinary for another reason. He married his niece, Uma Roy. While that was accepted, and even favored, in some communities in India, it was frowned upon in Bengal’s Anglicized middle-class society. Einstein, it should be noted, married his cousin. Roy had become close to Uma even before he went to London. They grew up together in the house in North Calcutta. They had much in common. Perhaps under his influence, she too studied physics and became a physics teacher at the Modern High School for Girls on Syed Amir Ali Avenue. When Roy went to London, she helped him financially. After he returned, the relationship deepened, producing turmoil in

Page 9 the family. But his elder brother, Himanshu, blessed the relationship. Roy and Uma married and had their first, and only child, a daugher they named Anjana. Himangshu invited them to come and live in his house. He had three sons, and his own health was declining. So Roy and Uma moved in and helped care for him. Less than a year later, Himangshu died. Roy and Uma took over responsi- bility for managing household affairs. Roy became surrogate father for the sons who remained at home.

PROBING THE FRONTIERS OF THEORETICAL PHYSICS In 1964 Roy was appointed Reader in the Pure Physics Department of the Cal- cutta University. With that promotion he was relieved of a lot of the classroom Roy with his niece, Uma, teaching. He used the freedom to pursue the latest theoretical developments in who was also a physics high energy physics. New particles continued to be detected one after another teacher. Courtesy Anjana Srivastava. as the particle accelerators in the big labs became ever more powerful. The physics of dispersion relations couldn’t keep up with this growing “particle zoo.” A number of leading physicists, including Salam and Matthews at Imperial College, placed their bets on the new theories based on the abstruse Lie Algebra of Special Unitary (SU) Groups. The power of group theory beyond SU(2) was just beginning to be appreciated, and was real- ized through flavor SU(3) as introduced by [Murray] Gell-Mann and [Yuval] Ne’eman. The Ω− [particle] needed to fill in the decuplet was found in 1963. The Gell-Mann–Zweig quark ideas had just been formulated, but were far from being completely accepted. There was no experimental evidence for quarks, and the ideas about color that allowed three quarks to make a nucleon only began to take form in 1964...Current algebra, a mixture of symmetry and some dynamics, was beginning to take shape with work by Nambu and Lurie but was still in the wings.43 Imperial College was an epicenter of these new theories. Had Roy gone to Imperial a little later, or stayed longer, he too would have been positioned to catch this wave. By that time Calcutta University was becoming marginal in the world of international physics. Roy had to follow these exciting developments from afar, and after the fact. One of his protégés in the Physics Department at that time recalls, He was thinking about physics more fundamental than he had yet done. He told me to study gravitation. So that is perhaps what occupied his mind, like the minds of many particle/field theorists of his generation, such as his good friend, John Charap.44 Charap arrived at Imperial College just after Roy had left and he worked with Salam, Tom Kibble and Ray Streater on the mathematics of spontaneous . This proved to be the stepping stone that Salam used to discover the “deep symmetries” that led to the unification of the nuclear weak and strong forces, a milestone achievement for which he shared with Sheldon Glashow and Stephen Weinberg the No- bel Prize in 1979. Charap went on to become an expert in the theory of covariant electrodynamics, which is vital for understanding relativistic field theory and . By this time S.N. Bose had left behind his research career and spent his semi-retirement engaged in ef- forts to promote higher education in India. But he and Roy remained very close. Roy’s daughter remembers seeing her father often with Bose: My memories of him [my father] are vivid - the childhood time spent with him and his pro- fessor, Satyen Bose, are so well etched in mind even today. The only thing I never understood then was that I was so fortunate to have seen them so close. I grew up knowing that baba [father] was a great personality, a versatile reader, and an erudite scientist. But unfortunately

Page 10 I did not have any opportunity to see and understand any of this by age ten.45

TURMOIL ON CAMPUS In 1967 the Naxalite upheaval began. The news of a peasant revolt in the Nax- albari district of convinced the Maoist wing of the Communist Party (Marxist) that the revolution was at last at hand. The Maoists split away and began training guerrillas for the revolution. Their call to arms electrified the A Naxalite rally in Calcut- students of Calcutta, especially at the campuses of Calcutta University. Many ta. The Maoist movement eventually splintered into of Roy’s graduate students got caught up in the fervor; some, like Dipanjan Rai rival factions that fought Chaudhuri, dropped out and went to the countryside to make a peasant revolu- each other in the streets. tion. Roy was sympathetic but critical. He was still a devout Trotskyist, though his political activity by then was pretty much confined to writing articles about world affairs and Marxist theory. He would go to the addas in the coffee shops around the university and argue that Mao was a revisionist. Dipanjan Rai Chaudhuri recalls: Politics were hotly debated He was as staunch a Trotskyite as his students were Maoists, and in the endless addas at the many an evening planned for tepid tea and physics developed into Coffee House in Calcutta. hot coffee and hotter polemics. Next day would find him prone, with [his little daughter] Munia walking down his pain and her mom changing hot water bags endlessly.46 The government crushed the Naxalites; many were killed and thousands jailed. Roy came to the aid of friends and former students, like Rai Chaudhuri. He hired lawyers for them out of his own pocket and often went to the jails to check on them. Rai Chaudhuri was eventually released on the condition that he leave the country immediately. Roy helped him get into a PhD program in physics in London. All of this took time and drained his energy.

A STRUGGLE TO KEEP TEACHING Roy continued to get radiation treatments. He had to use a cane to walk. Adding to his misery, he developed a duodenal ulcer, which he thought had come from eating too much spicy Bengali food. , who was a Junior Scientist in the department at that time, recalls: I had the privilege to learn much physics directly from him. He was a very friendly and help- ful person. But by 1964 he was already suffering from spinal problems. Although he used to come to the Science College regularly, I found him bogged down with health problems, not only his own but also of his older brother [Himangshu] who finally died. He took teaching seriously, but I think he lost interest in doing original research himself.47 Roy derived immense satisfaction from teaching and mentoring his graduate students. And by all ac- counts, they returned and respect and affection that he gave them. He was very fond of his students and was always happy to engage in discussions on all sorts of topics imaginable, ranging from politics to quantum theory. He was interested in knowing his students at a personal level and was never short of empathy. I recall that he always used his own brand of humor to keep himself in the background.48 In 1974 Roy began to suffer fevers and had symptoms of jaundice. The doctors he consulted tried dif- ferent treatments. None worked. Finally, a close relative, Dr. Anil Sensharma, was able to get him admitted

Page 9 to the Eastern Command Military Hospital in Alipur. The doctors recommended exploratory surgery. They found and removed a cancerous cyst on his pancreas. He had to remain in the hospital for about ten months. During his recuperation, Roy read everything he could about pancreatic diseases. He concluded that he must have pancreatic cancer. He discovered that patients who had received radiation treatment for ankylos- ing spondilytis often developed cancers about ten years after the treatments began.49 That also explained his ulcer. He had been taking strong anti-inflammatory medicine for years to reduce his pain.

A MATCHLESS MASTERPIECE FROM HIS DEATHBED Meanwhile, preparations were underway for a symposium to celebrate the 50th anniversary of Bose Statis- tics. The organizers were soliciting speakers and papers. Roy wanted very much to be a part of this tribute to his mentor and friend. But he was bedridden at that point. One of the organizers of the event recalled: [I] was then running helter skelter to find somebody to provide material on Bose for the 50th anniversary of Bose statistics. I found that most people who claimed to know Bose’s work were empty vessels. Then someone suggested I go to Dr. Purnangshu Roy for the task. So I did. He was quite ill then, unable to sit up. At being asked, he first started to laugh. Then he said he did not know how much he would be able to help. In the event Dr. Roy’s illness prevented him from writing the paper. But through that brief encounter, I got a good glimpse into the abstruse area of Bose Statistics. I went to Dr. Roy again in 1974 with the request that he write a paper on the background against which the Bose Statistics was born, what the Statistics were, and what the likely ben- efit the future generation would obtain from the Statistics. I said the only condition was that it should not have a single line of mathematics – that it be understandable to the layman. Dr. Roy was then terminally ill. Despite this, he managed to hand me a paper which was on the one hand fluid in language, beautifully clear, and on the other hand masterly in exposition of the statistics of Bose. It has remained matchless over the years.50

A DIALECTICIAN IN PHYSICS AND POLITICS This essay, titled “Thermal radiation laws, Bose Statistics, and its immediate impact,” was published in the journal Science and Culture.51 It is a tour de force. In just 20 pages Roy traced the historic development of radiation physics from the groundbreaking work of Ludwick Boltzman in the nineteenth century up to the birth of quantum mechanics. He showed how scientific advances come “dialectically,” in fits and starts, and often through the clash of contradictory ideas. The Bose Statistics are a good example. Bose was led to his breakthrough not by philosophical reason- ing (“dialectical” or otherwise) but by what he called a “crazy idea.” , who was then only 23 years old, had just published a paper on the interaction of radiation with free electrons. He had derived a mathematical expression for the probability of a Compton interaction (scattering) between an electron and a photon. The expression had two parts. The first depended on the radiation density of the primary fre- quency alone, while the second depended on the radiation density of the frequency that arose as a result of the Compton process. In other words, the probability that something would happen depended on something that had yet to happen! That was just the beginning of the “crazy ideas.” Wave-particle duality (complementarity), limits to the precision of certainty in the atomic realm, time reversal, — all these “crazy ideas” turned out to be true. Such are the “dialectics of nature.”

Page 12 TERMINAL CANCER In September, 1975 Roy became sick again. Another surgery revealed that the cancer had spread. The doctors said his situation was hopeless and gave him medication for pain. His old friend, Partha Ghose, recounts the last time he saw Roy: “I went to see him in hospital a few days before he passed away. He held my hand, and closed his eyes with tears running down his cheeks. I am glad I could give him some solace at that time.” 52 Purnangshu Kumar Roy died around midnight on September 19, 1975 with his wife at his side. The Bengali weekly Desh published an obituary prominently on the editorial page. The article cited his ac- complishments and concluded, “Dr. Roy was a ‘thorough’ man, as much in science as in other areas he had interests in - literature, music, sports and addas. He charmed his students, professors, anybody and everybody he met.”53

CONCLUSION I asked Dipanjan Rai Chaudhuri how he would sum up the life and accomplishments of P.K. Roy. I cannot do better than what he wrote in response: In the matter of research in the theoretical physics of particles P.K. Roy was sharing the depression of his peers all over the world, consequent to the refusal of the high-energy in- finities in to go away. Even after the spectacular successes of the Stan- dard Model, quantum field theory, the only analytical theory of quantum fields, remained unsatisfactory. It would be wrong to think that P.K. Roy went into some sort of hibernation. He continued to participate in the construction of the Standard Model. A PhD student of his worked with Feynman’s partons. And like others of his peers he prepared himself, as far as his pain allowed, for an onslaught on gravity. He was a rugged man, a fighter. Life had dealt him a raw deal, but he fought the fates right to the Command Hospital, coaxing out chocolates from Munia [his daughter] on his death-bed, explaining clinically his condition to his visitors, and even allowing the occasional student visitor to act as a nurse for him... P.K. Roy was no mere Bengali scientific gentry. Indeed, we had lived beside a Titan, if we consider all the dimensions of his life and his intensity in living them all.54

Dr. P.K. Roy with wife, Uma, and daughter, Anjana, in their home in Calcutta - the last family photo before he died. Courtesy Anjana Srivastava.

Page 11 NOTES

1 C.W. Ervin, “Purnangshu Kumar Roy: Protégé and Friend of S. N. Bose,” in G. Gangopadhyay and A. Kundu (eds.), CU Physics 100 (2016), 175-78. 2 Email from Mukul Roy, October 1, 2015. Mukul Roy is the nephew of late Purnangshu Roy. He resides in Calcutta. 3 For an account of the Indian Trotskyist party, including Roy’s role, see C.W. Ervin, Tomorrow is ours: the Trotskyist move- ment in India and Ceylon, 1935-1948 (2006). 4 Letter of recommendation, signed by John Kellas, Principal, March 29, 1952. Private collection of Anjana Srivastava. She is the daughter and only child of late P.K. and Uma Roy. She resides in Mumbai. 5 S. Chatterjee and E. Chatterjee, Satyendra Nath Bose (1976), p.68. See also: K.C. Wali (ed.), Satyendra Nath Bose: His Life and Times (2009), xxxiv; and Jagadish Sharma, “Satyendra Nath Bose,” Physics Today 27:4 (April 1974), 129-30. 6 Mahadev Dutta received his PhD in Applied Mathematics from Calcutta University in 1950. He went to the Indian Institute of Technology, where he worked on number theory, topology, and statistical physics. His publications include Bose Statis- tics—Emergence, Essence and Effect (1974). See Festschrift for Professor Mahadev Dutta, Proceedings of the 65th birth anniversary symposia in honor of Mahadeva Dutta (1987). Jagadish Sharma received his PhD in physics in 1953 from Calcutta University, joined the faculty of the Indian Institute of Technology, Kharagpur, and went on to research positions at Princeton University and Brookhaven National Laboratory. In 1981 he became a Principal Scientist in the Research Depart- ment of the US Navy’s White Oak Laboratory, where he developed techniques in X-ray Photoelectron Spectroscopy. 7 Purnima Sinha (nee Sen Gupta) graduated from Scottish Churches College and went on to the Rajabazar Science College. Working under Bose, she received her PhD on X-ray and differential thermal analysis of Indian clay minerals in 1957. She married the eminent anthropologist Professor Surajit Sinha. They went to the US and in 1963-64 she worked at Stanford University for Howard Pattee, a theoretical biologist who was investigating the origin of life. After her return to India, she worked at the Bose Institute and the Central Glass and Ceramic Research Institute. She was actively engaged in . Her publications include An Approach to the study of Indian music (1970) and studies of the musicians, Gopal Ghosh, and Jnan Prakash Ghosh. She eventually became a musician, painter, and sculptor in her own right. She died in 2015. Ashoke K. Bose started in and joined S.N. Bose’s team in the Khaira Lab. He worked with Purnima Sinha on X-ray and they co-authored the paper, “X-Ray and Differential Thermal Studies of some Indian Montmorillonites” (Nature, July 1954). He then went to work under in Europe. In the 1960s he became a professor in the Physics Depart- ment of the Université de Montréal, Canada. Birendra Chandra Dutta and his fellow researcher, Anjan K. Ghose, built the now famous spectrophotometer that gave more precise measurements of thermoluminescence afterglow spectra. He went to Birkbeck College in England and studied under David Butt, who had been a student of . Dutta got his PhD for solving a problem in β-ray spectroscopy. He became a professor at Birkbeck and in the 1960s worked at CEA [Atomic Energy Commission] in Saclay, France. Anjan K. Ghosh went to Itek Corporation in the US (a Defense Department contractor) and then to the Argonne National Lab in the 1960s. 8 P. Sinha, “Satyen Bose in Berlin,” website of S.N. Bose Project. https://sites.google.com/site/snbproject/purnimasinha. Also: Purnima Sinha, Bijnan Sadhanar Dhdray Satendra Nath Bose (1981). 9 Chatterjee and Chatterjee, ibid., p.65. 10 Email from Dipanjan Rai Chaudhuri, November 6, 2015. Rai Chaudhuri did his MSc in physics and started his doctoral pro- gram at Calcutta University under P.K. Roy in the late 1960s. Like many other brilliant Bengali youth of that era, he enthu- siastically responded to the call of the Maoist party (Naxalites) to leave his “bourgeois” life in Calcutta and foment peasant revolution in the countryside. That chapter in his life is recounted in V.S. Naipaul’s India: A Million Mutinies Now (1990). He was arrested and jailed. P.K. Roy helped to secure his release. He was set free on the condition that he immediately leave the country. He went to London and earned a PhD. Upon his return, he became professor and subsequently the head of the Department of Physics at Presidency College. 11 Amalkumar Raichaudhury, Atmajigyasa o Anyanya Rachana [Self-questions and other writings] (2007). After earning his MSc Raychaudhuri spent four years doing experimental work. During that time he taught himself differential geometry and general relativity. In 1952 he went to work at the Indian Association for the Cultivation of Science (IACS). Meghnad Saha was the Director from 1953 to his death in 1956; S.N. Bose moved his office to the IASC in 1959. Raichaudhuri wanted to pursue Relativity theory but was put to work instead on the properties of metals. Working on his own, he derived and in 1955 published the equation which is now named for him. While leading physicists abroad recognized the significance of his work, the physics establishment in India barely took notice. In 1959 he submitted a PhD dissertation and two years later was hired by Presidency College. His theoretical work was not widely recognized in India until the 1970s. 12 In QED the infinite number of possible virtual processes are handled mathematically by a power-expansion series of the type, 2 4 6 a0 + a1g + a2g +a3g … where the terms after the leading order (a0) are incremental refinements. In the case of an electron interacting with its own field the expansion parameter, g, is a small fraction (e2/ ħc ≈ 1/137). Since raising a fraction expo-

Page 14 nentially gives a much smaller number, each successive term in the series after a0 should shrink. However, as Oppenheimer discovered in 1930 when he tried to calculate the transition states that the electron goes through in emitting and absorbing photons, he found that the series diverged logarithically. Renormalized QED provided the apparatus to eliminate only one infinity at a time. To solve the overlapping infinity problem Salam transferred the mathematics from four-dimensional space- time to a less familiar four-dimensional momentum space, where he could associate every possible infinity on a one-to-one basis with a single sub-integration and then subtract them, leaving the final integrals convergent. His solution was part of his PhD thesis, “Renormalization of Quantum Field Theory” (1951). For general background see R.L. Mills, “Tutorial on infinities in QED,” in L. Brown (ed.), Renormalization: from Lorentz to Landau (and beyond) (1993), pp. 59-84; Cao and Schweber, “The conceptual foundations and the philosophical aspects of renormalization theory,” Synthese 97 (1993) 33-108; and H. Genz, Nothingness: the Science of empty space (1999). 13 Raymond F. Streater submitted his PhD thesis, “The Quantum Theory of Fields,” in 1960. He became a lecturer at Princeton and then a professor of physics at Imperial and later at King’s College in London. Tom Kibble became Professor of Physics at Imperial, where he co-discovered (along with and C. R. Hagen) the and Higgs in 1965-67 and introduced the concept of cosmic strings into cosmology in 1995. Claud Lovelace never finished his PhD but became a Senior Fellow at CERN, where he worked on Chew-Mandelstam dispersion relations and subsequently settled at Rutgers University in New Jersey, where he made a breakthrough contribution to string theory. Riazuddin held faculty positions at Rochester, Pennsylvania, and the University of Chicago and then returned to his native Pakistan, where he joined the Quaid-i-Azam University’s Institute of Physics and played a key role in Pakistan’s nuclear weapons program. Muham- mad Munirul Islam became an Assistant Professor of Research at Brown University and then joined the Physics Department at the University of Connecticut, where he remained until retiring in 2007. Ashok Kumar Gupta became a professor in the Physics Department at Allahabad University. In the early 1970s, at the invitation of Salam, he did a research sabbatical at the International Centre for Theoretical Physics in Trieste. D.K. Guha became a specialist in cryogenics in the Department of Chemical Engineering at the Indian Institute of Technology, Kharagpur. Erasmus M. Ferreira worked at the Stanford Linear Accelerator Center and became a professor at the Pontifícia Universidade Católica in Rio de Janeiro. 14 Email from E. Ferreira, February 27, 2016. 15 R. Streater, http://www.mth.kcl.ac.uk/~streater/wightman.html. Arthur Wightman was one of the founders of modern mathematical physics. He created a mathematically elegant and axiomatic approach to quantum field theory in which all the important physical results, such as the parity-charge-time (PCT) symmetry and the connection between spin and statistics, be- came theorems. Streater, recalls: “I was introduced to Wightman’s paper, 1956, by P. K. Roy, then, in 1957 like me, a Ph. D. student of Abdus Salam at Imperial College. I had asked Salam ‘What is a quantised field?’ and received the answer, ‘Good. I was afraid you would ask me something I did not know. A quantised field, phi(x) at the point x of space-time, is that operator assigned by the physicist using the correspondence principle, to the classical field phi at the point x’. I went away thinking about this. Then I realised that what I needed was a statement of which operator is assigned by the physicist. I complained to P. K. Roy, who said that I should read Wightman’s paper.” The paper was “Quantum field theory in terms of vacuum expecta- tion values,” Physical Review 101 (1956) 860-866. 16 The quantum mechanical properties “spin,” “angular momerntum,” and “parity” can be confusing, since they do not cor- respond to the same terms in . Spin (S) is an intrinsic form of angular momentum, an “internal” quantum property that is unrelated to macrophysical rotation in space. The existence of spin angular momentum was inferred from experiments in which particles were observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone. Wolfgang Pauli proposed the concept and then worked out the mathematics in 1927. Spin is given as a dimensionless spin quantum number, a non-negative integer or half integer. Orbital Angular Momentum (L) is a quantum op- erator related to the rotation of a particle around its own axis, somewhat like a corkscrew. Total Angular Momentum (J) is the operator that combines both the Spin and the Orbital Angular Momentum of a particle or quantum system. J = L + S. Parity is the symmetry of reflection: what happens to a particle when you reverse its spatial coordinate system. If the mirror reflected version of an allowed reaction is also an allowed reaction, we say that parity is conserved. 17 Quoted in M. Gardner, “The Fall of Parity,” in The Ambidextrous Universe (1964). 18 Quoted in G. Fraser, Cosmic anger: Abdus Salam – the first Muslim Nobel scientist (2008), 139. 19 Salam also assigned problems in dispersion relations to Riazuddin, E. Ferreira, and M. Islam. Riazuddin used dispersion relations for Compton scattering of virtual photons off pions to analyze their charge radius: “Charge radius of pion,” Physi- cal Review 114:4 (1959) 1184–86. He subsequently used nucleon-nucleon dispersion relations to discriminate proton-proton scattering in the pseudoscalar meson: “Low-energy p-p scattering phase shifts and dispersion relations,” Physical Review 121 (1961) 5. E. Ferreira studied K+-meson-deuteron inelastic scattering, using impulse approximation to determine the phase- shifts for the isotopic spin state: “On the coupling between (Λ, p) field and the K-meson field, Nuovo Cimento 8:2 (1958) 359-360; “K+-Deuteron scattering in the impulse approximation,” Physical Review 115 (15 September 1959) 1727; “The attractive K−-meson proton interaction,” Nuovo Cimento 11:6 (1959) 880-881; and “On the inelastic scattering of mesons by deuterons,” Annals of Physics 16: 2 (1961) 235-62. M. Islam used the Salam/Matthews and Igi equations to tackle the prob- lem of the parity of the K-mesons. M. Islam, “The parity of K-mesons and dispersion relations,” Nuovo Cimento 13:1 (1959) 224-27.

Page 15 20 T. Kibble, “Abdus Salam at Imperial College,” in M. Duff (ed.), Salam + 50 (2007), p.8. 21 P.K. Roy studied the two seminal papers that Bose had written on statistical physics in 1924. For background see P. Ghosh, “Bose statistics: A historical perspective,” in C.K. Majumdar, P. Ghose, E. Chatterjee, S. Bandyopadhyay and S. Chatterjee (eds.), S. N. Bose: The man and his work. Part II (1994) 35-71. 22 Y. Eisenberg, W. Koch, E. Lohrmann, M. Nikolic, M. Schneeberger, and H. Winzeler, “Interactions and decays of K–-me- sons,” Nuovo Cimento 9:5 (September 1958), 745-79; and G.B. Chadwick, S.A. Durrani, P.B. Jones, J.W. Wignall, and D.H. Wilkinson, “Observations of K–-meson interactions in nuclear emulsion,” Philosophical Magazine 3:35 (November 1958), 1193-1212. 23 Isospin, like Spin, is something of a misnomer. Isospin (or isobaric spin) is a quantum q-number (operator) related to electric charge, not to rotation in space. A particle having different charge states but the same mass is defined as having the same iso- spin. The proton and neutron, for example, are the same particle in two isospin states; the mesons K–, K+, K0 are one particle in three isospin states. Angular momentum is related to spin. The total angular momentum of a particle, J, is the sum of its spin angular momentum, S, and its orbital angular momentum, L. The conservation of angular momentum applies to J, but not to the components S and L. 24 Andrew Pickering, Constructing Quarks: A sociological history of particle pjhysics (1984) . 25 A. Salam and W. Gilbert, “On generalised dispersion relations. II,” Nuovo Cimento 10:3 (1956), 607-611. Salam and Mat- thews also presented papers on dispersion relations to the Seventh Annual Rochester Conference in 1957. See L. Koester, G. Ascoli, G. Feldman, R. Newton, W. Riesenfeld, M. Ross, and R. Sachs (eds.), High Energy Nuclear Physics: Proceedings of the Seventh Annual Rochester Conference, April 15-19, 1957. 26 M.L. Goldberger, M.T. Grisaru, S.W. MacDowell, and D.Y. Wong, “Theory of low-energy nucleon-nucleon scattering,” Physical Review 120:6 (1960) 2250. 27 P.K. Roy, “K–-meson absorption in nuclei, an isobaric spin and angular momentum analysis,” Nuclear Physics 9 (1958/59) 314-325. 28 M.M. Block, E.B. Brucker, I.S. Hughes, T. Kikuchi, C. Meltzer, F. Anderson, A. Pevsner, E.M. Harth, J. Leitner, and H.O. Cohn, “Observation of He4 hyperfragments from K–-He interactions: The K–-Λ relative parity,” Physical Review Letters 3:6 (15 September 1959), 291. The team directed a beam of K–-mesons into a bubble chamber. The interaction produced a π–-meson and a Helium hyperfragment. The He4 and the hyperfragment both have positive parity; the π–-meson has nega- tive (odd) parity. So, for parity to be conserved, the incoming K–-meson also would have to have negative parity to balance. 29 R.D. Tripp, M.B. Watson, and M. Ferro-Luzzi, “Determination of the Σ parity,” Physical Review Letters 8:4 (1962) 175; M.M. Block, L. Lendinara, and L. Monari, Proceedings of the International Conference on High-Energy Nuclear Physics at CERN (1962) 371; H. Courant et al., “Determination of the relative Σ – Λ parity,” Physical Review Letters 10 (1963) 409. 30 In 1959 Saul Barshay, a post doc working at the Institute for Theoretical Physics in Copenhagen, followed the same approach in his analysis of the simpler case of K-meson scattering off a single nucleon. S. Barshay, “Low-type integral equations for the absorption and production of K mesons,” Nuclear Physics 13:3 (1959) 435-46. 31 Reported in the Sixth Session (“Strange Particle Interactions”) of the Seventh Annual Rochester Conference (1957). L. Koester et. al., op. cit., 6:1-37. 32 P.K. Roy, “Low-energy application of relativistic K–-meson-nucleon dispersion relations,” Physical Review Letters, 2:8 (April 1959), 364-365. 33 P.T. Matthews and A. Salam, “The inelastic scattering of elementary particles,” Nuovo Cimento 13:2 (1959), 381-93. Also W. Alles, “Dispersion relation analysis of P-wave K-meson nucleon scattering,” Nuovo Cimento 19:3 (1961), 600-604. 34 Purnansukumar Ray, “Some Topics in Elementary Particle Physics,” October 1, 1959. 131 pages. The thesis is held at Central Library, Imperial College, South Kensington campus, London. 35 P. Ray, op. cit., 122. 36 Chatterjee and Chatterjee, ibid., 77-78. 37 P.K. Roy, “K– -meson-nucleon scattering and relativistic dispersion relations,” Nuclear Physics 20 (1960), 417-439. Cited: M. M. Islam, “K-meson-nucleon scattering,” Nuovo Cimento 20:3 (1961), 546-552. 38 P.K. Roy, “On relativistic dispersion relations,” Proceedings of the National Institute of Sciences of India A 28:2 (1962) 226. 39 Padmanabha Dasgupta studied meson theory. He continued at the Saha Institute of Nuclear Physics in Calcuta, where he co-authored papers with Salil Roy, who also earned his PhD in particle physics at Calcutta University. Dasgupta also published papers on kaon-nucleon scattering with B. Dutta-Roy, a Princeton PhD who returned home in the sixties. Dasgup- ta eventually became Professor of Physics at University of Kalyani and was affiliated to the S.N. Bose National Centre for Basic Science. 40 Personal communication with Lokenath Debnath, October 28, 2015. Dr. Debnath received his PhD in Pure Mathematics from Calcutta University in 1965 and a DIC and PhD in Applied Mathematics from London University in 1967. He is Professor in the Department of Mathematics, University of Texas Pan-American, Edinburg, Texas. 41 Email from Indrani Bose, February 16, 2016. 42 Email from Dipanjan Rai Chaudhuri, November 6, 2015. 43 G.S. Guralnik, “The history of the Guralnik, Hagen and Kibble development of the theory of spontaneous symmetry breaking and guage particles,” International Journal of A, 24 (2009) p. 2603. 44 Email from D. Rai Chaudhuri, op. cit. 45 Email from Anjana Srivastava, July 31, 2015. 46 Email from D. Rai Chaudhuri, op. cit. 47 Emails from Parthasarathi Ghose, March 3 and June 28, 2015. Partha Ghose became Professor at the S.N. Bose National Centre for Basic Sciences in Kolkata. In addition to his research publications he has written numerous popular books on science, appeared in the Indian TV shows, Quest and Eureka, and received the National Award for the Best Science and Technology coverage in the Mass Media for 1986–1990. An accomplished musician, he promotes the arts; he has served as Chairman of the Film and Television Institute and Board member of the Academy of Fine Arts, Kolkata. 48 Email from Avijit Lahiri, April 27, 2016. 49 W.M. Court-Brown and R. Doll, “Mortality from cancer and other causes after radiotherapy for ankylosing spondylitis,” British Medical Journal 2 (1965), 1327-32. 50 Editorial in Desh [Kolkata] October 18, 1975. 51 P.K. Roy, “Thermal Radiation Laws, Bose Statistics and Its Immediate Impact,” Science and Culture 40:7 (July 1974), 271- 294. 52 Email from P. Ghose, March 3, 2015. 53 Desh, ibid. 54 Email from D. Rai Chaudhuri, April 17, 2016.