DOCSLIB.ORG

Advanced Quantum Mechanics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Advanced Quantum Mechanics F. J. Dyson ADVANCED QUANTUM MECHANICS Second Edition arXiv:quant-ph/0608140v1 18 Aug 2006 ADVANCED QUANTUM MECHANICS Lecture notes by Professor F. J. Dyson for a course in Relativistic Quantum Mechanics given at Cornell University in the Fall of 1951. Second Edition The first edition of these notes was written by Professor Dyson. The second edition was prepared by Michael J. Moravcsik; he is responsible for the changes made in the process of re-editing. Generally used notation: A∗ : complex conjugate transposed (Hermitian conjugate) A+ : complex conjugate (not transposed) ∗ ∗ A : A β = A γ4 = adjoint A−1 = inverse AT = transposed I = identity matrix or operator i Table of Contents Introduction 1 SubjectMatter ...................................... ........ 1 DetailedProgram.................................... ......... 2 OneParticleTheories ................................ .......... 2 The Dirac Theory 4 TheFormoftheDiracEquation . .......... 4 LorentzInvarianceoftheDiracEquation . ............... 6 ToFindtheS......................................... ...... 7 TheCovariantNotation .. .. .. .. .. .. .. .. .. .. .. .. .. .......... 8 ConservationLaws–ExistenceofSpin . .............. 9 ElementarySolutions. .. .. .. .. .. .. .. .. .. .. .. .. .. ........... 10 TheHoleTheory...................................... ....... 11 PositronStates–chargeconjugation . ............... 11 ElectromagneticPropertiesof the Electron . ................. 12 TheHydrogenAtom .................................... ....... 13 Solutionoftheradialequation . ............. 14 Behavior of an Electron in non-relativistic approximation ...................... 17 Summary of Matrices in the Dirac Theory in our notation . ................. 20 Summary of Matrices in the Dirac Theory in the Feynman notation ................ 21 Scattering Problems and Born Approximation 22 GeneralDiscussion .................................. .......... 22 ProjectionOperators. .. .. .. .. .. .. .. .. .. .. .. .. .. ........... 23 CalculationofSpurs ................................. .......... 24 Scattering of two electrons in Born Approximation – The MøllerFormula ............. 27 Relation of Cross Sections to Transition Amplitudes . ................... 29 ResultsforMøllerScattering . ............. 30 NoteontheTreatmentofExchangeEffects . ............. 31 Relativistic Treatment of Several Particles . ................... 31 Field Theory 32 ClassicalRelativisticFieldTheory . ................ 32 QuantumRelativisticFieldTheory . .............. 34 TheFeynmanMethodofQuantization . ............ 35 TheSchwingerActionPrinciple. ............. 36 A.TheFieldEquations ................................ ...... 37 B. The Schr¨odinger Equation for the State-function . ................. 37 C.OperatorFormoftheSchwingerPrinciple . ............ 38 D.CanonicalCommutationLaws . ........ 39 E. The Heisenberg Equation of Motion for the Operators . .............. 39 F.GeneralCovariantCommutationLaws . .......... 39 G.AnticommutingFields .. .. .. .. .. .. .. .. .. .. .. .. .. ....... 40 ii Examples of Quantized Field Theories 41 I.TheMaxwellField.................................. ......... 41 MomentumRepresentations . ........ 42 FourierAnalysisofOperators . .......... 43 EmissionandAbsorptionOperators . .......... 44 GaugeInvarianceoftheTheory. ......... 45 TheVacuumState ..................................... .... 45 TheGupta-BleulerMethod . ....... 47 Example: Spontaneous Emission of Radiation . ............. 47 TheHamiltonianOperator . ....... 49 FluctuationsoftheFields . ......... 50 The Lamb Shift – Fluctuation of Position of Electron . ............... 51 Ia. TheoryofLineShiftandLineWidth. ............. 52 TheInteractionRepresentation . ........... 53 Application of Interaction Representation to Line Shift andLineWidth ........... 54 Calculation of Line Shift – Non-Relativistic Theory . ................. 57 TheIdeaofMassRenormalization . ......... 57 II. Field Theory of the Dirac Electron – Without Interaction .................... 59 CovariantCommutationRules . ........ 60 MomentumRepresentations . ........ 61 FourierAnalysisofOperators . .......... 62 EmissionandAbsorptionOperators . .......... 62 ChargeSymmetricalRepresentation . ........... 63 TheHamiltonian ..................................... ..... 64 Failure of Theory with Commuting Fields . ........... 64 TheExclusionPrinciple . .. .. .. .. .. .. .. .. .. .. .. .. ........ 65 TheVacuumState ..................................... .... 65 III. Field Theory of Dirac Electron in External Field . ................... 66 CovariantCommutationRules . ........ 66 TheHamiltonian ..................................... ..... 68 AntisymmetryoftheStates . ........ 69 PolarizationoftheVacuum . ........ 70 CalculationofMomentumIntegrals. ........... 73 PhysicalMeaning of the Vacuum Polarization . ............. 75 Slowly Varying Weak Fields. The Uehling Effect. ............. 78 IV. Field Theory Of Dirac And Maxwell Fields In Interaction . ................... 78 The Complete Relativistic Quantum Electrodynamics . ............... 78 FreeInteractionRepresentation . ............ 80 Free Particle Scattering Problems 81 A.MøllerScatteringofTwoElectrons . .............. 81 Properties of the DF Function .................................. 82 TheMøllerFormula–Conclusion. ......... 83 Electron-PositronScattering. ............ 84 B. Scattering of a Photon by an Electron – The Compton Effect – The Klein-Nishina Formula. 84 CalculationofCrossSection. .......... 86 SumOverSpins....................................... .... 87 C.Two-QuantumPairAnnihilation . ............ 90 D. Bremsstrahlung and Pair Creation in the Coulomb Field of anAtom .............. 92 iii General Theory of Free Particle Scattering 94 ReductionofanOperatortoNormalForm . ............ 96 FeynmanGraphs...................................... ....... 98 FeynmanRulesofCalculation. ............ 100 TheSelf-EnergyoftheElectron. ............. 102 Second-Order Radiative Corrections to Scattering . .................... 104 Treatment of Low-Frequency Photons – The Infra-Red Catastrophe. ................ 116 Scattering By A Static Potential 118 A.TheMagneticMomentoftheElectron . ............ 121 B. Relativistic Calculation of the Lamb Shift . ................. 123 CovariantPartoftheCalculation. ........... 124 Discussion of the Nature of the Φ-Representation . ............... 126 Concluding Non-Covariant Part of the Calculation . ............... 127 AccuracyoftheLambShiftCalculation . ........... 130 Typist’s Afterword 132 Notes 134 References 138 Index 140 iv Lecture Course 491 — Advanced Quantum Theory F. J. Dyson — Fall Semester 1951 Introduction Books W. Pauli, “Die Allgemeinen Principien der Wellenmechanik”; Handbuch der Physik, 2 ed., Vol. 24, Part 1; Edwards reprint, Ann Arbor 1947. (In German) [1] W. Heitler, Quantum Theory of Radiation, 2nd Edition, Oxford. 3rd edition just published. [2] G. Wentzel, Introduction to the Quantum Theory of Wave-Fields, Interscience, N.Y. 1949 [3] I shall not expect you to have read any of these, but I shall refer to them as we go along. The later part of the course will be new stuff, taken from papers of Feynman and Schwinger mainly. [4], [5], [6], [7], [8] Subject Matter You have had a complete course in non-relativistic quantum theory. I assume this known. All the general principles of the NR theory are valid and true under all circumstances, in particular also when the system happens to be relativistic. What you have learned is therefore still good. You have had a course in classical mechanics and electrodynamics including special relativity. You know what is meant by a system being relativistic; the equations of motion are formally invariant under Lorentz transformations. General relativity we shall not touch. This course will be concerned with the development of a Lorentz–invariant Quantum theory. That is not a general dynamical method like the NR quantum theory, applicable to all systems. We cannot yet devise a general method of that kind, and it is probably impossible. Instead we have to find out what are the possible systems, the particular equations of motion, which can be handled by the NR quantum dynamics and which are at the same time Lorentz–invariant. In the NR theory it was found that almost any classical system could be handled, i.e.quantized. Now on the contrary we find there are very few possibilities for a relativistic quantized system. This is a most important fact. It means that starting only from the principles of relativity and quantization, it is mathe- matically possible only for very special types of objects to exist. So one can predict mathematically some important things about the real world. The most striking examples of this are: (i) Dirac from a study of the electron predicted the positron, which was later discovered [9]. (ii) Yukawa from a study of nuclear forces predicted the meson, which was later discovered [10]. These two examples are special cases of the general principle, which is the basic success of the relativistic quantum theory, that A Relativistic Quantum Theory of a Finite Number of Particles is Impossible. A RQ theory necessarily contains these features: an indefinite number of particles of one or more types, particles of each type being identical and indistinguishable from each other, possibility of creation and annihilation of particles. Thus the two principles of relativity and quantum theory when combined lead to a world built up out of various types of elementary particles, and so make us feel quite confident that we are on the right way to
Load more

Recommended publications
  • Preliminary Acknowledgments
    PRELIMINARY ACKNOWLEDGMENTS The central thesis of I Am You—that we are all the same person—is apt to strike many readers as obviously false or even absurd. How could you be me and Hitler and Gandhi and Jesus and Buddha and Greta Garbo and everybody else in the past, present and future? In this book I explain how this is possible. Moreover, I show that this is the best explanation of who we are for a variety of reasons, not the least of which is that it provides the metaphysical foundations for global ethics. Variations on this theme have been voiced periodically throughout the ages, from the Upanishads in the Far East, Averroës in the Middle East, down to Josiah Royce in the North East (and West). More recently, a number of prominent 20th century physicists held this view, among them Erwin Schrödinger, to whom it came late, Fred Hoyle, who arrived at it in middle life, and Freeman Dyson, to whom it came very early as it did to me. In my youth I had two different types of experiences, both of which led to the same inexorable conclusion. Since, in hindsight, I would now classify one of them as “mystical,” I will here speak only of the other—which is so similar to the experience Freeman Dyson describes that I have conveniently decided to let the physicist describe it for “both” of “us”: Enlightenment came to me suddenly and unexpectedly one afternoon in March when I was walking up to the school notice board to see whether my name was on the list for tomorrow’s football game.
    [Show full text]
  • Measurements of Elastic Electron-Proton Scattering at Large Momentum Transfer*
    SLAC-PUB-4395 Rev. January 1993 m Measurements of Elastic Electron-Proton Scattering at Large Momentum Transfer* A. F. SILL,(~) R. G. ARNOLD,P. E. BOSTED,~. C. CHANG,@) J. GoMEz,(~)A. T. KATRAMATOU,C. J. MARTOFF, G. G. PETRATOS,(~)A. A. RAHBAR,S. E. ROCK,AND Z. M. SZALATA Department of Physics The American University, Washington DC 20016 D.J. SHERDEN Stanford Linear Accelerator Center , Stanford University, Stanford, California 94309 J. M. LAMBERT Department of Physics Georgetown University, Washington DC 20057 and R. M. LOMBARD-NELSEN De’partemente de Physique Nucle’aire CEN Saclay, Gif-sur- Yvette, 91191 Cedex, France Submitted to Physical Review D *Work supported by US Department of Energy contract DE-AC03-76SF00515 (SLAC), and National Science Foundation Grants PHY83-40337 and PHY85-10549 (American University). R. M. Lombard-Nelsen was supported by C. N. R. S. (French National Center for Scientific Research). Javier Gomez was partially supported by CONICIT, Venezuela. (‘)Present address: Department of Physics and Astronomy, University of Rochester, NY 14627. (*)Permanent address: Department of Physics and Astronomy, University of Maryland, College Park, MD 20742. (C)Present address: Continuous Electron Beam Accelerator Facility, Newport News, VA 23606. (d)Present address: Temple University, Philadelphia, PA 19122. (c)Present address: Stanford Linear Accelerator Center, Stanford CA 94309. ABSTRACT Measurements of the forward-angle differential cross section for elastic electron-proton scattering were made in the range of momentum transfer from Q2 = 2.9 to 31.3 (GeV/c)2 using an electron beam at the Stanford Linear Accel- erator Center. The data span six orders of magnitude in cross section.
    [Show full text]
  • Richard Phillips Feynman Physicist and Teacher Extraordinary
    ARTICLE-IN-A-BOX Richard Phillips Feynman Physicist and Teacher Extraordinary The first three decades of the twentieth century have been among the most momentous in the history of physics. The first saw the appearance of special relativity and the birth of quantum theory; the second the creation of general relativity. And in the third, quantum mechanics proper was discovered. These developments shaped the progress of fundamental physics for the rest of the century and beyond. While the two relativity theories were largely the creation of Albert Einstein, the quantum revolution took much more time and involved about a dozen of the most creative minds of a couple of generations. Of all those who contributed to the consolidation and extension of the quantum ideas in later decades – now from the USA as much as from Europe and elsewhere – it is generally agreed that Richard Phillips Feynman was the most gifted, brilliant and intuitive genius out of many extremely gifted physicists. Here are descriptions of him by leading physicists of his own, and older as well as younger generations: “He is a second Dirac, only this time more human.” – Eugene Wigner …Feynman was not an ordinary genius but a magician, that is one “who does things that nobody else could ever do and that seem completely unexpected.” – Hans Bethe “… an honest man, the outstanding intuitionist of our age and a prime example of what may lie in store for anyone who dares to follow the beat of a different drum..” – Julian Schwinger “… the most original mind of his generation.” – Freeman Dyson Richard Feynman was born on 11 May 1918 in Far Rockaway near New York to Jewish parents Lucille Phillips and Melville Feynman.
    [Show full text]
  • Disturbing the Memory
    1 1 February 1984 DISTURBING THE MEMORY E. T. Jaynes, St. John's College, Cambridge CB2 1TP,U.K. This is a collection of some weird thoughts, inspired by reading "Disturbing the Universe" by Freeman Dyson 1979, which I found in a b o okstore in Cambridge. He reminisces ab out the history of theoretical physics in the p erio d 1946{1950, particularly interesting to me b ecause as a graduate student at just that time, I knew almost every p erson he mentions. From the rst part of Dyson's b o ok we can learn ab out some incidents of this imp ortant p erio d in the development of theoretical physics, in which the present writer happ ened to b e a close and interested onlo oker but, regrettably, not a participant. Dyson's account lled in several gaps in myown knowledge, and in so doing disturb ed my memory into realizing that I in turn maybein a p osition to ll in some gaps in Dyson's account. Perhaps it would have b een b etter had I merely added myown reminiscences to Dyson's and left it at that. But like Dyson in the last part of his b o ok, I found it more fun to build a structure of conjectures on the rather lo ose framework of facts at hand. So the following is o ered only as a conjecture ab out how things mighthave b een; i.e. it ts all the facts known to me, and seems highly plausible from some vague impressions that I have retained over the years.
    [Show full text]
  • Neutron Scattering
    Neutron Scattering Basic properties of neutron and electron neutron electron −27 −31 mass mkn =×1.675 10 g mke =×9.109 10 g charge 0 e spin s = ½ s = ½ −e= −e= magnetic dipole moment µnn= gs with gn = 3.826 µee= gs with ge = 2.0 2mn 2me =22k 2π =22k Ek== E = 2m λ 2m energy n e 81.81 150.26 Em[]eV = 2 Ee[]V = 2 λ ⎣⎡Å⎦⎤ λ ⎣⎦⎡⎤Å interaction with matter: Coulomb interaction — 9 strong-force interaction 9 — magnetic dipole-dipole 9 9 interaction Several salient features are apparent from this table: – electrons are charged and experience strong, long-range Coulomb interactions in a solid. They therefore typically only penetrate a few atomic layers into the solid. Electron scattering is therefore a surface-sensitive probe. Neutrons are uncharged and do not experience Coulomb interaction. The strong-force interaction is naturally strong but very short-range, and the magnetic interaction is long-range but weak. Neutrons therefore penetrate deeply into most materials, so that neutron scattering is a bulk probe. – Electrons with wavelengths comparable to interatomic distances (λ ~2Å ) have energies of several tens of electron volts, comparable to energies of plasmons and interband transitions in solids. Electron scattering is therefore well suited as a probe of these high-energy excitations. Neutrons with λ ~2Å have energies of several tens of meV , comparable to the thermal energies kTB at room temperature. These so-called “thermal neutrons” are excellent probes of low-energy excitations such as lattice vibrations and spin waves with energies in the meV range.
    [Show full text]
  • Freeman Dyson, Visionary Technologist, Is Dead
    2/28/20, 12:42 Page 1 of 10 https://nyti.ms/2TshCWY Freeman Dyson, Visionary Technologist, Is Dead at 96 After an early breakthrough on light and matter, he became a writer who challenged climate science and pondered space exploration and nuclear warfare. By George Johnson Feb. 28, 2020 Updated 3:30 p.m. ET Freeman J. Dyson, a mathematical prodigy who left his mark on subatomic physics before turning to messier subjects like Earth’s environmental future and the morality of war, died on Friday at a hospital near Princeton, N.J. He was 96. His daughter Mia Dyson confirmed the death. His son, George, said Dr. Dyson had fallen three days earlier in the cafeteria of the Institute for Advanced Study in Princeton, “his academic home for more than 60 years,” as the institute put it in a news release. As a young graduate student at Cornell University in 1949, Dr. Dyson wrote a landmark paper — worthy, some colleagues thought, of a Nobel Prize — that deepened the understanding of how light interacts with matter to produce the palpable world. The theory the paper advanced, called quantum electrodynamics, or QED, ranks among the great achievements of modern science. But it was as a writer and technological visionary that he gained public renown. He imagined exploring the solar system with spaceships propelled by nuclear explosions and establishing distant colonies nourished by genetically engineered plants. “Life begins at 55, the age at which I published my first book,” he wrote in “From Eros to Gaia,” one of the collections of his writings that appeared while he was a professor of physics at the Institute for Advanced Study — an august position for 2/28/20, 12:42 Page 2 of 10 someone who finished school without a Ph.D.
    [Show full text]
  • Compton Sources of Electromagnetic Radiation∗
    August 25, 2010 13:33 WSPC/INSTRUCTION FILE RAST˙Compton Reviews of Accelerator Science and Technology Vol. 1 (2008) 1–16 c World Scientific Publishing Company COMPTON SOURCES OF ELECTROMAGNETIC RADIATION∗ GEOFFREY KRAFFT Center for Advanced Studies of Accelerators, Jefferson Laboratory, 12050 Jefferson Ave. Newport News, Virginia 23606, United States of America kraff[email protected] GERD PRIEBE Division Leader High Field Laboratory, Max-Born-Institute, Max-Born-Straße 2 A Berlin, 12489, Germany [email protected] When a relativistic electron beam interacts with a high-field laser beam, the beam electrons can radiate intense and highly collimated electromagnetic radiation through Compton scattering. Through relativistic upshifting and the relativistic Doppler effect, highly energetic polarized photons are radiated along the electron beam motion when the electrons interact with the laser light. For example, X-ray radiation can be obtained when optical lasers are scattered from electrons of tens of MeV beam energy. Because of the desirable properties of the radiation produced, many groups around the world have been designing, building, and utilizing Compton sources for a wide variety of purposes. In this review paper, we discuss the generation and properties of the scattered radiation, the types of Compton source devices that have been constructed to present, and the future prospects of radiation sources of this general type. Due to the possibilities to produce hard electromagnetic radiation in a device small compared to the alternative storage ring sources, it is foreseen that large numbers of such sources may be constructed in the future. Keywords: Compton backscattering, Inverse Compton source, Thomson scattering, X-rays, Spectral brilliance 1.
    [Show full text]
  • Iasinstitute for Advanced Study
    IAInsti tSute for Advanced Study Faculty and Members 2012–2013 Contents Mission and History . 2 School of Historical Studies . 4 School of Mathematics . 21 School of Natural Sciences . 45 School of Social Science . 62 Program in Interdisciplinary Studies . 72 Director’s Visitors . 74 Artist-in-Residence Program . 75 Trustees and Officers of the Board and of the Corporation . 76 Administration . 78 Past Directors and Faculty . 80 Inde x . 81 Information contained herein is current as of September 24, 2012. Mission and History The Institute for Advanced Study is one of the world’s leading centers for theoretical research and intellectual inquiry. The Institute exists to encourage and support fundamental research in the sciences and human - ities—the original, often speculative thinking that produces advances in knowledge that change the way we understand the world. It provides for the mentoring of scholars by Faculty, and it offers all who work there the freedom to undertake research that will make significant contributions in any of the broad range of fields in the sciences and humanities studied at the Institute. Y R Founded in 1930 by Louis Bamberger and his sister Caroline Bamberger O Fuld, the Institute was established through the vision of founding T S Director Abraham Flexner. Past Faculty have included Albert Einstein, I H who arrived in 1933 and remained at the Institute until his death in 1955, and other distinguished scientists and scholars such as Kurt Gödel, George F. D N Kennan, Erwin Panofsky, Homer A. Thompson, John von Neumann, and A Hermann Weyl. N O Abraham Flexner was succeeded as Director in 1939 by Frank Aydelotte, I S followed by J.
    [Show full text]
  • Works of Love
    reader.ad section 9/21/05 12:38 PM Page 2 AMAZING LIGHT: Visions for Discovery AN INTERNATIONAL SYMPOSIUM IN HONOR OF THE 90TH BIRTHDAY YEAR OF CHARLES TOWNES October 6-8, 2005 — University of California, Berkeley Amazing Light Symposium and Gala Celebration c/o Metanexus Institute 3624 Market Street, Suite 301, Philadelphia, PA 19104 215.789.2200, [email protected] www.foundationalquestions.net/townes Saturday, October 8, 2005 We explore. What path to explore is important, as well as what we notice along the path. And there are always unturned stones along even well-trod paths. Discovery awaits those who spot and take the trouble to turn the stones. -- Charles H. Townes Table of Contents Table of Contents.............................................................................................................. 3 Welcome Letter................................................................................................................. 5 Conference Supporters and Organizers ............................................................................ 7 Sponsors.......................................................................................................................... 13 Program Agenda ............................................................................................................. 29 Amazing Light Young Scholars Competition................................................................. 37 Amazing Light Laser Challenge Website Competition.................................................. 41 Foundational
    [Show full text]
  • Advanced Information on the Nobel Prize in Physics, 5 October 2004
    Advanced information on the Nobel Prize in Physics, 5 October 2004 Information Department, P.O. Box 50005, SE-104 05 Stockholm, Sweden Phone: +46 8 673 95 00, Fax: +46 8 15 56 70, E-mail: [email protected], Website: www.kva.se Asymptotic Freedom and Quantum ChromoDynamics: the Key to the Understanding of the Strong Nuclear Forces The Basic Forces in Nature We know of two fundamental forces on the macroscopic scale that we experience in daily life: the gravitational force that binds our solar system together and keeps us on earth, and the electromagnetic force between electrically charged objects. Both are mediated over a distance and the force is proportional to the inverse square of the distance between the objects. Isaac Newton described the gravitational force in his Principia in 1687, and in 1915 Albert Einstein (Nobel Prize, 1921 for the photoelectric effect) presented his General Theory of Relativity for the gravitational force, which generalized Newton’s theory. Einstein’s theory is perhaps the greatest achievement in the history of science and the most celebrated one. The laws for the electromagnetic force were formulated by James Clark Maxwell in 1873, also a great leap forward in human endeavour. With the advent of quantum mechanics in the first decades of the 20th century it was realized that the electromagnetic field, including light, is quantized and can be seen as a stream of particles, photons. In this picture, the electromagnetic force can be thought of as a bombardment of photons, as when one object is thrown to another to transmit a force.
    [Show full text]
  • The Matter-Antimatter Dipole Ray Fleming 101 E State St
    The Matter-Antimatter Dipole Ray Fleming 101 E State St. #152 Ithaca NY 14850 Physicists have known that mechanical forces can be described by a set of equations that are similar to Maxwell’s equations since Oliver Heaviside first proposed it in 1893.[1] His and most subsequent theories attempt to combine gravity with electromag- netism, but run into difficulties because there is no negative mass or negative gravity to form a dipole analogous to the electric charge dipole. Gravity also works in the wrong di- rection. In 1930 Paul Dirac interpreted the solutions to the equation bearing his name as forms of positive and negative energy, even though there is no negative energy in stand- ard physics theory. A few years later these were identified as matter and antimatter. His speculative thoughts on the behavior of this positive and negative “energy” were analo- gous to the characteristics of a dipole.[2] In the years that followed we have learned that all forms of matter exhibit short-range repulsion, which is normally attributed to the Pauli exclusion principle. Additionally, matter and antimatter can be thought to have a strong short-range attraction just prior to annihilation. As such, matter and antimatter are known to participate in force interactions consistent with a dipole, and this paper examines some of our scientific knowledge that supports the existence of the matter-antimatter dipole. 1. Introduction was the birth of the theory of gravitomagnetism, which has since been developed by numerous other While mechanical forces are not normally listed as scientists.[3][4][5][6] It has, however, never achieved one of the four fundamental forces of the standard mainstream acceptance due to two major inherent dif- model, physicists have nonetheless attempted to unify ficulties.
    [Show full text]
  • Lecture: April 1, 2020 the Matter of Antimatter: Answering the Cosmic
    Lecture: April 1, 2020 The Matter Of Antimatter: Answering The Cosmic Riddle Of Existence: Brian Green and then Discussion with Brian Greene as a the moderator Quantum Field Theory (QFD) – The Ultimate Theory of Quantum Particles Firstly, trying to picture electron as a wave causes lot of headaches... These waves are clearly not ordinary waves – they are not like ripples on the surface of water... Despite all this, Schodinger¨ wave theory or its relativisic version, Dirac theory, has been very successful. However, at end of 1920, physicist realized that it told only part of the truth... (a) It only describes how particles move. It cannot handle physics when particles are created and destroyed, as happens when a radioactive element decays or when electron and positron annihilate each other, creating photons.... (b) Recall the g- factor : e e ~ Magnetic moment of an electron is µ = g m S = g m 2 . Dirac theory predicted g = 2. This was good to explain all the spilling of energies. Shelter island conference in 1947 Organizer was Robert Oppenheimer. The cost of the conference was about 890 dollars. All well known physicists were invited... 1 . Physicist Rabi’s precise measurement of g-factor showed that g is ONLY APPROXIMATELY equal to 2. He found the g value to be equal to g = 2:00244 He know the precise error bars of his experiment and was certain that g equal to 2 is only an approximation. This led to the notion of Quantum Fields. (1920)s: Particles are described by Wave Equations. This cannot describe creation and annihilation of particles (1930)s : Particles are described by Fields: Quantum Field Theory– It can describe creation-annihilation of particles.
    [Show full text]