arXiv:1709.00711v1 [physics.hist-ph] 3 Sep 2017 hmi eal n16–9Iwssiltkn ore,bt7%o ytim my of 75% but courses, taking still source was the I sourcery. wen missed 1968–69 and to had Tsai, devoted In Wu-yang was I from case detail. notes the my c in got In for them sub I the but Lagrangians speak. of 1967–68, effective most to in learn on course so to notes knee, had students short master’s elect the quantum few the usual, on as a one so as [3], t including well symmetry [1], which as subject in point, [2], the theory that on namics field At out to No papers Theory. two approach his Source had in new removed, given a apparently had invented were he advice infinities and the 1965 taken in had He Lecture disciples. twelve of group uin o e a oie h a ih o e a vnnvrhe never Feynman. even w of had work icon I the to me. unlike me for Harvard, right for to was but came who I choice sphe idea before no a no Schwinger was for had of effect I there see Casimir So had You the he Julian. later). of with (although calculation more share place heroic which to the a willing about over to was Boyer all he Tim ideas was long guided no Glashow around had Shelly be Coleman and not Sydney would students, th finish. so would to and and Harvard, me Professor by for Although Assistant tenure adv an granted research but insight. be my was not be and he Pip to elegance that Frank Callan realized Curt Julian’s from quickly asking by year of away momentarily previous the thought blown in the had Mec only course, Quantum course 251, was that of Physics It Julian, taken was, from had that. course a I at on although ones in sat good I very that 1968 not courses, taking just aeHrad al CAYas(1968-1981) Years UCLA Early Harvard, Late uinwsvr ae otk nsuet,adIimdaeyjie h joined immediately I and students, on take to eager very was Julian aet avr sagaut tdn n16,adtefis yea first the and 1967, in student graduate a as Harvard to came I eiicne fJla Schwinger: Julian of Reminiscences etme ,2017 5, September .A Milton A. K. 1 through t etfrom ject 98 he 1968, enough hanics, was I r erefore alof Fall theory i.I kin. sr I isor, rody- hiral just ard bel ith re, he is e I In those days, Schwinger lectured three days a week, nominally 12:00– 1:00, but he invariably was late, arriving in his Iso Rivolta about 12:15, and the lectures ran later and later, approaching 2pm. I remember one occasion when Julian was teaching Quantum Mechanics, a course in which half the audience were undergraduates, whose Houses stopped serving lunch at 2. One day he asked, rhetorically, “If I could just have a few minutes more?” and was met with a Harvard hiss. He stormed out, only to encounter a locked door, so he had to slink out the side, but never again (at least that year) lectured beyond 1:30. His dozen graduate students could only meet him on Wednesday after- noon, after he returned from lunch. One year Roman Jackiw was visiting Harvard, so they often had lunch together, and sometimes they never re- turned. Julian’s secretary would put out a list for students to sign up to see him at 9am, and we would stagger in as close as possible to that time (since we had stayed up all night trying to prepare for our audience with the great man) because if you were near the top of the list, you would likely get in to see him before he left at 6, but if you were number 10, you would probably fail to do so. Once admitted to his sanctum, Julian gave you his complete attention, of course, ignoring the telephone, and allowing you to explain what you had been doing the last week or two, and getting up to where you were stuck. Invariably, he would make an insightful suggestion of how to proceed. It might not always work, but it would take a week at least to follow the suggestion through. There was never any feeling of time constraint in the meetings, again proving the necessity for being at the top of the sign-up list. Early on, Julian suggested I look at spectral forms for scattering, what were conventionally called dispersion relations, but derived by looking at causal processes and then performing “space-time extrapolation.” It was a very effective method of getting results. My first real project was rederiving the using these methods, a nice pedagogical project. I was to present that at my oral examination, probably in Spring 1969. I had just barely got launched, talking about the basic concepts of source theory I would use in the calculation when Paul Martin objected, and before I could say anything, Julian responded, and then went to the board for a 30 minute exposition. I think I may have been allowed to say a few words about my conclusions, but then I was ushered out for the committee’s deliberation. I must have passed, because Julian gave me a copy of his just-published Brandeis lectures on source theory [4].

2 The other topic he suggested for my thesis was looking at the quantum coupling of and photons to gravity. This was about the time of the discovery of Callan, Coleman, and Jackiw of the “new, improved” stress ten- sor for scalar fields, the conformal stress tensor [5]. I again investigated this using spectral forms. At first, I had not defined the basis tensors quite cor- rectly, so I asked a stupid question of Sydney Coleman at the Erice Summer School in 1970, because I didn’t initially see the advantage of the conformal tensor. But fortunately I discovered the error while I was completing my thesis, and my published results were an early manifestation of the trace [6]. In the Spring of 1970, Julian and Clarice took a sabbatical in Japan. To keep his group together, Richard Ivanetich, his student who had become another non-permanent Assistant Professor at Harvard, gave a course on source theory, and so we kept ourselves going. But when Julian returned in the Fall, having completed his first source-theory book [7], he met his assembled students with a bombshell: He had finally accepted David Saxon’s entreaties and had decided to move to UCLA, much to the dismay for his Boston-born wife Clarice. We students were all greatly disheartened. But then, when I had my private meeting with him, Julian explained that he had arranged for me to come along as a postdoc, together with Lester DeRaad, Jr., and Wu-yang Tsai. The latter were really more than ready to defend, but I was stunned, because I had expected to have another year to finish up. I was not ready to leave civilized Cambridge for the wilderness of California. I worked hard that Fall, and moved out to California in February 1971, where I finished writing up my thesis. Julian and Clarice had arrived a week earlier, to be greeted by the great San Fernando earthquake. Why did Julian decide to leave Harvard? The fact that the reception of source theory by his colleagues and former students at Harvard was rather frosty was a contributor, but Julian always stated positive reasons: He wanted to move to a gentler climate, where he could play tennis every day, and swim, as well as ski occasionally. Formerly famously overweight, he had become obsessed with becoming more fit after his imperfect idol succumbed to pancreatic cancer in 1958. The Schwingers bought a house in Bel Air, with a beautiful view of the city of Los Angeles, of course with a pool. Clarice’s mother, Sadie, had her own apartment in their house. Saxon and Schwinger both presumed that students would continue to flock to him on the West Coast: he had had some 70 students at Harvard, and was to spend the last 23 years of his life at UCLA, but the influx of students was

3 not to be. The students there were clearly not so talented as the Harvard co- terie, and by 1971 Julian’s work had fallen out of fashion. At UCLA, Julian had no more than five students, including Walter Wilcox, who became my first postdoc at Oklahoma State, now at Baylor, and Luis Fernando Urrutia, now professor at UNAM in Mexico City. My thesis defense was even less trying than my oral exam. By this point, Julian and I had decamped to UCLA, and Julian took the local committee and me to a French restaurant. (Harvard had very flexible rules about the composition of doctoral committees.) I successfully answered Julian’s only question, “where were you born?,” and from that point I only had to deal with the hazards of long-distance transmittal of my dissertation to Harvard, navigating the new technologies of the Xerox machine (Harvard had a secret, unpublished rule about that), and the lack of FedEx in those days! I officially became an Assistant Research /Assistant Visiting Professor at UCLA in Fall 1971. In those days, almost all postdocs at UCLA taught two courses per year. (My future father-in-law, Alfredo Ba˜nos, Jr., who became Vice-Chair, once published a chart showing the monotonic de- crease of the student faculty ratio with faculty rank, with the postdocs having the heaviest teaching load.) But my higher status did mean that I had much more intimate contact with Julian; whereas as a student I only saw him as a brilliant lecturer and bi-weekly mentor, at UCLA we had weekly lunches at various venues, and we were occasionally invited to the Schwingers’ home. These informal meetings were wonderful, full of discussions of physics and its culture. At dinner, Julian was a gracious host, drawing out quiet individuals to join in the conversation. He was never one to flaunt his deep erudition. I remember one dinner where he sat next to my wife’s nephew who was a sulky teenager, and Julian got him into the conversation by asking him about Thelonious Monk, one of the boy’s heroes. Not only did more social contact occur after the phase transition into being a postdoc, but also collaboration ensued. Julian very seldom worked on projects his students were involved in, but working with his “assistants” was another matter. So in 1974 when the discovery of the J/ψ particle was announced, Julian immediately came up with an explanation, in terms of a previously hidden sector [8], and suggested this might have something to do with dyons [9], particles having both magnetic and electric charge. Although these explanations ultimately proved unsatisfactory, and fell to the idea that

4 the J/ψ was a bound state of charmed and anti-charmed quarks,1 Julian did invite his postdocs into a convincing explanation of the decay ψ(3.7) into the J/ψ state [11]. (This work resulted in an ugly break in relations with former student Asim Yildiz.) And after giving a heuristic derivation of precession tests in general relativity [12, 13], he invited me to follow on with an analysis of the Lense-Thirring effect [14]. After the source theory book he wrote while he was on sabbatical in Tokyo in 1970 [7], Julian invited us three postdocs (and likely Jack Ng, who had come from Harvard to UCLA to finish his Ph.D. with Julian) to proofread the second volume. It was inadvertence, not an intentional slight, that led him to neglect to thank us in the preface to the resulting volume, which came out in 1973 [15]. We jointly wrote a very pretty paper on nonrelativistic dyon-dyon scattering [16], which included as co-author D. C. Clark, one of Julian’s few UCLA students. Personally, a stellar point of my life was my introduction to Margarita Ba˜nos by Clarice. Julian and Margarita’s father Alfredo Ba˜nos had been colleagues at the Radiation Laboratory at MIT during World War II, working together on the theory of radar. This work proved crucial for Julian’s later discovery of in , which was the basis of his [17]. Alfredo had moved to UCLA soon after the war, as had David Saxon, who had written up Julian’s lectures on microwave theory given at the end of the war, which eventually, in edited form, came to life in Electromagnetic Radiation [18]. In 1972 Clarice had arranged a dinner party for my postdoctoral colleague Lester DeRaad and Margarita, which did not go well, Lester particularly objecting to the blind date. (Margarita and Lester are now on good terms.) Some six weeks later, Clarice tried again with me, but this time just suggesting I call Margarita for a date. Don the Beachcomber, and a voyage surprise through the Santa Monica mountains later (with an interruption for Margarita dancing in New York), Margarita and I became a couple, married in 1978. Schwinger’s last substantial work in high-energy physics concerned an analysis of the scaling properties observed at Stanford in deep-inelastic scat- tering of electrons and on nucleons [19, 20]. Rather than inter- preting these in terms of Feynman’s partons, which later got conflated with quarks, he adopted a more phenomenological viewpoint, describing them in

1Julian detested quarks, partly because Gell-Mann had invented them. He provided a critique of their naming in his earlier Science article proposing a magnetic model of matter [10].

5 terms of double spectral forms, related to the Deser-Gilbert-Sudarshan rep- resentation [21, 22, 23, 24, 25]. We postdocs joined in [26, 27], but eventually, toward the end of our extended tenure at UCLA, we discovered that although the structure of the spectral forms was valid, in general the spectral region was not confined to positive mass distributions, which rendered conclusions suspect [28]. Somewhat earlier, he had returned to the subject he had mastered during the war, synchrotron radiation, adopting a quantum viewpoint [29], and this work led to collaborative papers with Tsai and Tom Erber [31, 30], who was a frequent visitor to our group at UCLA in the mid 1970s, invariably referring to Schwinger as (Big) Julie, reminiscent of what Oppenheimer had done back in the 1940s. Just before his “source-theory revolution” Schwinger had written on the subject of magnetic charge [32, 33, 34]. He immediately thereafter put the theory in source theory language [35], and followed this with a proposal that matter is composed of dyons [10], a name he coined to describe particles car- rying both electric and magnetic charge, an intriguing idea in place of quarks. The subject of magnetic charge he revisited in 1975 [36], bemoaning, “If only the Price had been right!”, referring to Buford Price’s discredited claim of discovering magnetic monopoles in Lexan sheets exposed to cosmic rays [37]. (Julian often worked with the TV on.) The following year, with such ex- periments in mind, we jointly revisited how magnetic charge interacted with electric charges, in a monumental paper on dyon-dyon scattering [16]. Two decades later, this work led to a new experiment with George Kalbfleisch [38], in turn inspired by Luis Alvarez’ searches in lunar samples [39]; our work set the best lower limit on masses for a decade until LHC data supplanted them [40, 41]. The reception of the high-energy physics community to Schwinger’s source- theory program was not warm; when not overtly hostile, the ideas were largely ignored. Julian’s reaction was to become ever more iconoclastic. He developed his own approach to the , based on the pho- ton propagation function [42, 43], reflecting his rejection of the the whole notion of renormalization, a concept which he had largely invented. (A more confrontational paper was never published; he increasingly turned to pub- lishing in the Proceedings of the National Academy, where he could publish without encountering hostile reviewing.) Although these ideas were largely rejected by the physics world, they did later spark some important insights into the running of the strong in QCD [44]. An even more

6 confrontational issue developed concerning the decay of the neutral pion into two photons, π0 → γγ. This had been initially explained by Schwinger back in 1951 in his most famous paper [45]; it is a manifestation of the axial-vector or chiral anomaly. This subject got rediscovered in the late 1960s; and in particular Adler and Bardeen proved that the anomaly was not subject to radiative corrections, but was given exactly by the lowest-order triangle dia- gram [46]. In 1972, we postdocs showed that the situation was rather more subtle, in that the pion decay process did possess higher-order QED correc- tions unless the pseudoscalar coupling is normalized at an infrared sensitive point [47]. The formal Adler-Bardeen theorem can, however, be maintained. Julian subsequently redid our calculation in his own, inimitable way, and obtained the same result that we did, a correction by a factor of 1 + α/(2π), where α is the fine-structure constant. But instead of seeking an accommo- dation with received wisdom, he chose to fight, and we wrote a joint paper. However, before we submitted it, Julian gave a talk at MIT on the subject, and was met with utter disdain. The paper was therefore never submitted to a journal, but a rather contentious section (subtitled “A Confrontation”) of the third (uncompleted) volume of Particles, Sources, and Fields, now in- cluded in the repackaged version of the latter part of the second volume plus the beginnings of the third, contains his iconoclastic calculation [48]. This unfortunate lost battle can be said to mark Schwinger’s end of involvement in high-energy physics proper, and the end of his attempt to complete his source theory program to include strong interactions. But Julian certainly did not reject all new ideas. He became fascinated by the ideas of , and its local version, supergravity, and in 1977 invited his former distinguished student Stan Deser, who had recently been one of the co-discoverers of supergravity, to UCLA to give a week of private lectures to his group, including Bob Finkelstein. Julian regretted he had not thought of the idea of fermion-boson unification, particularly since he had long before set up the key ingredients, such as the multispinor formulation and Grassmann variables. After this command performance Julian wrote his own version of supersymmetry [49]; Bob and I followed with a rederivation of supergravity [50]. But this reconstructive work had negligible impact. Most important for my later career, Julian learned about the Casimir effect from Seth Putterman, and immediately set about seeing how he could derive it without using the offensive idea of zero-point energy. After a short solo note [51], this led to two very substantial joint papers, one devoted to rederiving the Casimir effect between parallel dielectric slabs, the so-called

7 Lifshitz theory [52], and the second to rederiving the result of Tim Boyer, as a student of Glashow at Harvard, that the Casimir self-stress on a perfectly conducting spherical shell of zero thickness is repulsive, not attractive as Casimir and everyone else had supposed [53]. This is a subject I have never left. During all this time at UCLA Julian taught brilliant courses. Of course, quantum mechanics, now for undergraduates, based on his Measurement Al- gebra approach. Berge Englert eventually turned this into a book [54]. And, for the first time since the war, he taught the graduate Classical Electrody- namics course. After we three postdocs had sat in on that for a while, we asked if we could write up the notes into a book. A draft was sent to W.H. Freeman, who accepted the proposal; this caused Julian to pay attention. He looked at our manuscript, decided he could greatly improve upon it, and spent the next decade doing so, teaching the subject several times, before abandoning the project before reaching radiation theory. So, after his death in 1994, I undertook to turn the old typescript and the multitudinous revi- sions into modern LATEX form; the book was published in 1999 [55], and has had modest success, but has hardly dented sales of Jackson [56]. Julian also wanted to communicate the excitement of science to a wider audience. His most notable efforts in this regard was in collaboration with the BBC, where, with George Abell, a UCLA astronomer, he designed a course on relativity, both special and general, for the Open University, entitled “Un- derstanding Space and Time.” Julian was very excited about this project, working on it from 1976–79, which resulted in a number of TV programs aired on BBC2, and occasionally in the United States. In Los Angeles they were aired in the early morning by KCET, not surprising since the release roughly coincided with the extremely successful KCET Cosmos series (1980), also co-produced by the BBC, hosted by the extremely engaging Carl Sagan. In contrast, Julian’s TV style appeared rather wooden. A lasting testament to this endeavor was the book Einstein’s Legacy [57], aimed at a popular audience. Julian, although he put in long hours at home working (never allowing himself to be interrupted by a telephone call), had outside interests. We have already mentioned his pleasure in frequent skiing trips, and he had weekly tennis matches (which he had learned from his student Asim Yildiz at Harvard) with Lester. Privately, he enjoyed playing the piano, but never when anyone was around. (“Anything worth doing, is worth doing badly,” except physics, of course.) And in 1975 he became the second-largest owner

8 in a vineyard in Northern California, the V. Sattui Winery, which has been remarkably successful since its relaunch in 1976. 1978 marked Schwinger’s 60th birthday. The UCLA Physics Department organized a Fest in Julian’s honor. I ended up being defacto chief organizer of that meeting, which, not surprisingly, included many luminous names. It resulted in a rather nice Festschrift volume [58], but the transcript of the wonderful talk given by Feynman at the banquet was not published until the Festshrift for Julian’s 70th birthday came out [59]. Julian was quite grumpy about the whole affair, because he saw it as a sort of retirement celebration. A few years later, at a meeting in Atlanta, where he received the Monie Ferst award from Sigma Xi, he publicly apologized to his former students, me, Ken Johnson of MIT, and Margie Kivelson of UCLA, for being ungracious. It is often asked whether Feynman and Schwinger got along. Certainly, they always behaved cordially at conferences, both recalling how in the early days of QED only by comparing each other’s completely orthogonal calcula- tions and seeing that they yielded precisely the same predictions were they themselves convinced that their tentative procedures were sound. But it is true that for nearly two decades the two shared Nobel laureates lived in the same metropolis and never socialized privately.2 Feynman made sev- eral overtures, suggesting that they meet at a restaurant somewhere between Pasadena and Bel Air, but Julian was stand-offish, and such an encounter never happened, I think to both men’s deep regret. This failure to connect was another mark of Julian’s extreme privacy. Eventually the group of “sourcerer’s apprentices” at UCLA broke up. Tsai left first to take up a faculty job a Coral Gables, returning to Southern California after a year to work at JPL. DeRaad left for a career in indus- try, first working for R&D Associates, and attempted with Tsai to found a defense-based firm in the 1980s, with Julian on the board of directors. I could have stayed on at UCLA indefinitely, but with little chance of a faculty appointment, I followed my wife Margarita to Ohio State, and then, after two years, landed a faculty job in Oklahoma State. Three years later Margarita got an Assistant Professorship at the University of Oklahoma, and I was able to secure a Professorship there in 1986, where I’ve been based ever since. I met Julian a few times after I officially resigned from UCLA in 1981.

2Berge Englert has told me that the Schwingers once invited Dick and his wife to dinner, which Dick greatly enjoyed until a second couple appeared. This spoiled the evening for the Feynmans, who had expected they were to be the only guests.

9 I invited him to give a public talk at Oklahoma State in 1984, and I tried to do the same when I moved to Norman. Of course, I attended his 70th Fest in 1988 [59], which was dedicated to the memory of Dick Feynman, who had just succumbed to cancer. In 1989 came the debacle of , and Julian, being ever the iconoclast, fell into it with an explanation, which was convincing to very few. Berge Englert helped him publish one of his papers on this, which was printed alongside a publisher’s disclaimer [60]. Eventually he came to realize his ideas, and cold fusion itself, could not be right, and he turned to a subject that undoubtedly had experimental support, sonoluminesence, again at the urging of Seth Putterman. He decided this must have something to do with the dynamical Casimir effect, and published several short notes in the PNAS [61]. Unfortunately, he forgot that I had written, while still at UCLA, a paper on the Casimir energy of a dielectric ball [62], which was rather the inverse of the problem he was considering, a bubble in water, so he developed to a certain extent his own treatment. When I last met him at the annual Christmas party given at the Ba˜nos’ home in 1993, he discussed his latest efforts in this direction, and indirectly suggested I join in. Tragically, this was not to be, because in the following February he was diagnosed with pancreatic cancer. After his death I continued to pursue the subject, but eventually, with my colleagues Jack Ng and Iver Brevik, demonstrated to our satisfaction, at least, that the Casimir effect, dynamical or not, could not be relevant to the copious light produced repeatedly during bubble collapse [63, 64]. So how do we assess the legacy of Julian Schwinger? He was, of course, a giant of 20th century physics, who completely dominated for a decade in the 1950s. His influence on physics in the 21st century is per- vasive, even if largely unrecognized by many, particularly in the younger gen- eration. The fact he had so many brilliant and influential students guarantees the impact of his school on future generations. The techniques he invented, from the quantum action principle, effective Lagrangians, the Schwinger- Keldysh method, commutator anomalies, proper time methods, and “Feyn- man” parameters, to name a few, underlie much of modern theoretical physics, and are often used in ignorance of their inventor. Of course, he made mis- takes and took wrong directions, but as Einstein said, “Anyone who has never made a mistake has never tried anything new.” And to every problem to which Julian turned his attention, he brought new insight and new tech- niques, often sparking a whole new field of endeavor. He remains a beacon, guiding us into the future.

10 For more about Julian Schwinger’s life and work see [65], with some updates in [66]. Acknowledgments: I thank Berge Englert for asking me to write this reminiscence, and for his close reading of the manuscript. I dedicate this note to Julian’s memory.

References

[1] J. Schwinger, “Particles and Sources,” Phys. Rev. 152, 1219 (1966). doi:10.1103/PhysRev.152.1219

[2] J. Schwinger, “Sources and Electrodynamics,” Phys. Rev. 158, 1391 (1967). doi:10.1103/PhysRev.158.1391

[3] J. Schwinger, “Chiral Dynamics,” Phys. Lett. 24B, 473 (1967). doi:10.1016/0370-2693(67)90277-8

[4] J. Schwinger, Particles and Sources, (Gordon and Breach, New York, 1968).

[5] C. G. Callan, Jr., S. R. Coleman and R. Jackiw, “A New Im- proved Energy-Momentum Tensor,” Ann. Phys. (N.Y.) 59, 42 (1970). doi:10.1016/0003-4916(70)90394-5

[6] K. A. Milton, “Quantum Corrections to Stress Tensors and Conformal Invariance,” Phys. Rev. D 4, 3579 (1971). doi:10.1103/PhysRevD.4.3579

[7] J. Schwinger, Particles, Sources, and Fields. Volume 1, (Addison- Wesley, Reading, Mass., 1970).

[8] J.. Schwinger, “Interpretation of a Narrow Resonance in e+-e− Annihi- lation,” Phys. Rev. Lett. 34, 37 (1975). doi:10.1103/PhysRevLett.34.37

[9] J. Schwinger, “Speculations Concerning the ψ Particles and Dyons,” Science 188, 1300 (1975). doi:10.1126/science.188.4195.1300

[10] J. Schwinger, “A Magnetic Model of Matter,” Science 165, 757 (1969). doi:10.1126/science.165.3895.757

11 [11] J. Schwinger, K. A. Milton, W. y. Tsai and L. L. DeRaad, Jr., “Reso- nance Interpretation of the Decay of ψ′(3.7) into ψ(3.1),” Phys. Rev. D 12, 2617 (1975). doi:10.1103/PhysRevD.12.2617

[12] J. Schwinger, “Precession Tests of General-Relativity—Source Theory Derivations,” Am. J. Phys. 42, 507 (1974).

[13] J. Schwinger, “Spin Precession—A Dynamical Discussion,” Am. J. Phys. 42, 510 (1974).

[14] K. A. Milton, “Dynamics of the Lense-Thirring Effect,” Am. J. Phys. 42, 911 (1974).

[15] J. Schwinger, Particles, Sources, and Fields. Volume II, (Addison- Wesley, Reading, MA, 1973).

[16] J. Schwinger, K. A. Milton, W. y. Tsai, L. L. DeRaad, Jr. and D. C. Clark, “Nonrelativistic Dyon-Dyon Scattering,” Ann. Phys. (N.Y.) 101, 451 (1976). doi:10.1016/0003-4916(76)90020-8

[17] J. Schwinger, “Quantum Electrodynamics - An Individual View,” J. Phys. Colloq. 43, no. C8, 409 (1982). doi:10.1051/jphyscol:1982826

[18] K. A. Milton and J. Schwinger, Electromagnetic Radiation: Variational Methods, and Accelerators (Springer, Berlin, 2006)

[19] E. D. Bloom, et al., “High-Energy Inelastic e-p Scattering at 6◦ and 10◦”. Phys. Rev. Lett. 23, 930 (1969). Bibcode:1969PhRvL..23..930B. doi:10.1103/PhysRevLett.23.930.

[20] M. Breidenbach, et al.. “Observed Behavior of Highly Inelastic -Proton Scattering”. Phys. Rev. Lett. 23, 935 (1969). Bib- code:1969PhRvL..23..935B. doi:10.1103/PhysRevLett.23.935.

[21] J. Schwinger, “Source Theory Viewpoints in Deep Inelastic Scattering,” Proc. Nat. Acad. Sci. 72, 1 (1975) [Acta Phys. Austriaca Suppl. 14, 471 (1975)]. doi:10.1007/978-3-7091-8424-0−9, 10.1073/pnas.72.1.1

[22] J. Schwinger, “Deep Inelastic Scattering of Leptons. Part 1.,” Proc. Nat. Acad. Sci. 73, 3351 (1976). doi:10.1073/pnas.73.10.3351

12 [23] J. Schwinger, “Deep Inelastic Scattering of Charged Leptons,” Proc. Nat. Acad. Sci. 73, 3816 (1976). doi:10.1073/pnas.73.11.3816

[24] J. Schwinger, “Deep Inelastic Sum Rules in Source Theory,” Nucl. Phys. B 123, 223 (1977). doi:10.1016/0550-3213(77)90460-6

[25] J. Schwinger, “Deep Inelastic Scattering and Pion-Nucleon Cross-Sections,” Phys. Lett. 67B, 89 (1977). doi:10.1016/0370- 2693(77)90814-0

[26] W. y. Tsai, L. L. DeRaad, Jr. and K. A. Milton, “Verification of Virtual Compton-Scattering Sum Rules in Quantum Electrodynamics,” Phys. Rev. D 11, 3537 (1975) Erratum: [Phys. Rev. D 13, 1144 (1976)]. doi:10.1103/PhysRevD.13.1144, 10.1103/PhysRevD.11.3537

[27] L. L. DeRaad, Jr., K. A. Milton and W. y. Tsai, “Deep Inelas- tic Neutrino Scattering: A Double Spectral Form Viewpoint,” Phys. Rev. D 12, 3747 (1975) Erratum: [Phys. Rev. D 13, 3166 (1976)]. doi:10.1103/PhysRevD.13.3166, 10.1103/PhysRevD.12.3747

[28] R. J. Ivanetich, W. y. Tsai, L. L. DeRaad, Jr., K. A. Milton and L. F. Ur- rutia, “Anomalous Spectral Regions In Source Theory,” in Themes in Contemporary Physics (Julian Schwinger’s Festschrift), eds. S. Deser, H. Feshbach, R. J. Finkelstein, K. A. Johnson, and P. C. Martin, North- Holland, Amsterdam, 1979, p. 233 [Physica 96A, 233 (1979)].

[29] J. Schwinger, “Classical Radiation of Accelerated Electrons. II. A Quantum Viewpoint,” Phys. Rev. D 7, 1696 (1973). doi:10.1103/PhysRevD.7.1696

[30] J. Schwinger, W. y. Tsai and T. Erber, “Classical and Quantum The- ory of Synergic Synchrotron-Cherenkov Radiation,” Ann. Phys. (N.Y.) 96, 303 (1976) [Ann. Phys. (N.Y.) 281, 1019 (2000)]. doi:10.1016/0003- 4916(76)90194-9

[31] J. Schwinger and W. y. Tsai, “New Approach to Quantum Cor- rections in Synchrotron Radiation,” Annals Phys. 110, 63 (1978). doi:10.1016/0003-4916(78)90142-2

[32] J. Schwinger, “Electric- and Magnetic-Charge Renormalization. I,” Phys. Rev. 151, 1048 (1966). doi:10.1103/PhysRev.151.1048

13 [33] J. Schwinger, “Electric- and Magnetic-Charge Renormalization. II,” Phys. Rev. 151, 1055 (1966). doi:10.1103/PhysRev.151.1055

[34] J. Schwinger, “Magnetic Charge and ,” Phys. Rev. 144, 1087 (1966). doi:10.1103/PhysRev.144.1087

[35] J. Schwinger, “Sources and Magnetic Charge,” Phys. Rev. 173, 1536 (1968). doi:10.1103/PhysRev.173.1536

[36] J. Schwinger, “Magnetic Charge and the Charge Condi- tion,” Phys. Rev. D 12, 3105 (1975). doi:10.1103/PhysRevD.12.3105

[37] P. B. Price, E. K. Shirk, W. Z. Osborne, L. S. Pinsky. “Evidence for the Detection of a Moving Magnetic Monopole,” Phys. Rev. Lett. 35 487 (1975). doi:10.1103/PhysRevLett.35.487

[38] G. R. Kalbfleisch, W. Luo, K. A. Milton, E. H. Smith and M. G. Strauss, “Limits on Production of Magnetic Monopoles Utilizing Samples from the D0 and CDF Detectors at the Tevatron,” Phys. Rev. D 69, 052002 (2004) doi:10.1103/PhysRevD.69.052002 [hep-ex/0306045].

[39] R. R. Ross, P. H. Eberhard, L. W. Alvarez and R. D. Watt, “Search For Magnetic Monopoles In Lunar Material Using An Electromagnetic Detector,” Phys. Rev. D 8, 698 (1973). doi:10.1103/PhysRevD.8.698

[40] http://pdg.lbl.gov/2017/reviews/rpp2016-rev-mag-monopole-searches.pdf

[41] B. Acharya et al. [MoEDAL Collaboration], “Search for Magnetic Monopoles with the MoEDAL Forward Trapping Detector in 13 TeV Proton-Proton Collisions at the LHC,” Phys. Rev. Lett. 118, no. 6, 061801 (2017) doi:10.1103/PhysRevLett.118.061801 [arXiv:1611.06817 [hep-ex]].

[42] J. Schwinger, “Photon Propagation Function: Spectral Analysis of Its Asymptotic Form,” Proc. Nat. Acad. Sci. 71, 3024 (1974).

[43] J. Schwinger, “Photon Propagation Function: A Comparison of Asymptotic Functions,” Proc. Nat. Acad. Sci. 71, 5047 (1974). doi:10.1073/pnas.71.12.5047

14 [44] K. A. Milton and I. L. Solovtsov, “Analytic in QCD and Schwinger’s Connection Between the and the Spectral Density,” Phys. Rev. D 55, 5295 (1997). doi:10.1103/PhysRevD.55.5295 [hep-ph/9611438]. [45] J. Schwinger, “On Gauge Invariance and Vacuum Polarization,” Phys. Rev. 82, 664 (1951). doi:10.1103/PhysRev.82.664 [46] S. L. Adler and W. A. Bardeen, “Absence of Higher-Order Corrections in the Anomalous Axial Vector Divergence Equation,” Phys. Rev. 182, 1517 (1969). doi:10.1103/PhysRev.182.1517 [47] L. L. Deraad, K. A. Milton and W. Y. Tsai, “Second Order Radiative Corrections to the Triangle Anomaly. I,” Phys. Rev. D 6, 1766 (1972). doi:10.1103/PhysRevD.6.1766 [48] J. Schwinger, Particles, Sources, and Fields, Vol. III (Addison-Wesley, Advanced Book Classics, 1989) ISBN-13: 978-0738200552. [49] J. Schwinger, “Multispinor Basis of Fermi-bose Transformations,” Ann. Phys. (N.Y.) 119, 192 (1979). doi:10.1016/0003-4916(79)90255-0 [50] K. A. Milton, L. F. Urrutia and R. J. Finkelstein, “Construc- tive Approach To Supergravity,” Gen. Rel. Grav. 12, 67 (1980). doi:10.1007/BF00756169 [51] J. Schwinger, “Casimir Effect in Source Theory,” Lett. Math. Phys. 1 43 (1975) [52] J. Schwinger, L. L. DeRaad, Jr., and K. A. Milton, “Casimir Effect in Dielectrics,” Ann. Phys. (N.Y.) 115, 1 (1978). [53] K. A. Milton, L. L. DeRaad, Jr. and J. Schwinger, “Casimir Selfstress on a Perfectly Conducting Spherical Shell,” Ann. Phys. (N.Y.) 115, 388 (1978). doi:10.1016/0003-4916(78)90161-6 [54] J. Schwinger, Quantum Mechanics: Symbolism of Atomic Measure- ments, Ed. B.-G. Englert (Springer, Berlin, 2001) ISBN 3-540-41408-8. [55] J. Schwinger, L. L. DeRaad, Jr., K. A. Milton, and W.-y. Tsai, Classical Electrodynamics (Perseus/Westview, New York, 1998) ISBN-13: 978- 0738200569.

15 [56] J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, New York, 1999) ISBN-13: 978-0471309321.

[57] J. Schwinger, Einstein’s Legacy: The Unity of Space and Time (Scientific American Library, W. H. Freeman, Vol. 16, 1985) [Reprinted by Dover, Mineola, NY, 1996, ISBN 0-486-41974-6].

[58] S. Deser, H. Feshbach, R. J. Finkelstein, K. A. Johnson, and P. C. Martin, Themes in Contemporary Physics: Essays in Honour of Julian Schwinger’s 60th Birhtday (North-Holland, Amsterdam, 1979) [Physica, 96A (1979)].

[59] S. Deser and R. J. Finkelstein, Themes in Contemporary Physics II: Essays in Honor of Julian Schwinger’s 70th Birthday (World Scientific, Singapore, 1989).

[60] J. Schwinger, “Nuclear Energy in an Atomic Lattice,” Z. Phys. D 15, 221 (1990).

[61] J. Schwinger, “Casimir Energy . . . ,” and “Casimir Light . . . ,” Proc. Nat. Acad. Sci. USA 89, 4091, 11118 (1992); 90, 958, 2105, 4505, 7285 (1993).

[62] K. A. Milton, “Semiclassical Electron Models: Casimir Selfstress in Dielectric and Conducting Balls,” Annals Phys. 127, 49 (1980). doi:10.1016/0003-4916(80)90149-9

[63] K. A. Milton and Y. J. Ng, “Observability of the Bulk Casimir Ef- fect: Can the Dynamical Casimir Effect be Relevant to Sonolumines- cence?,” Phys. Rev. E 57, 5504 (1998) doi:10.1103/PhysRevE.57.5504 [hep-th/9707122].

[64] I. H. Brevik, V. N. Marachevsky and K. A. Milton, “Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to ,” Phys. Rev. Lett. 82, 3948 (1999) doi:10.1103/PhysRevLett.82.3948 [hep-th/9810062].

[65] J. Mehra and K. A. Milton, Climbing the Mountain: The Scientific Biography of Julian Schwinger (Oxford, 2000) ISBN 0 19 850658 9.

16 [66] K. A. Milton, “Julian Schwinger: Nuclear Physics, the Radiation Lab- oratory, Renormalized QED, Source Theory, and Beyond,” Phys. Per- spect. 9, 70 (2007) doi:10.1007/s00016-007-0326-6 [physics/0610054].

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