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Mukhin R. R. Richard Feynman and Julian Schwinger and condensed matter physics in the soviet union. Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, iss. 5, pp. 113-141. DOI: 10.18500/0869-6632-2018-26-5-113-141

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Richard Feynman and Julian Schwinger and condensed matter physics in the soviet union

Autors: 
Mukhin Ravil Rafkatovich, Stary Oskol technological Institute. A. A. Ugarov (branch) of Federal state educational institution of higher professional education "national research technological University "MISIS" (STI nust Misa)
Abstract: 

Aim. The aim of the paper is to study the impact of the works of R. Feynman and J. Schwinger on the development of condensed matter physics in the Soviet Union in the end 1940s and early 1960s. Method. The research is based on the analysis of original works with the use of available literature concerning the issue under consideration. Results. The transfer of the methods of quantum field theory to the many-body problem was a very complex and nontrivial task. The main contribution to its solution was made by physicists from the environment of L.D. Landau. The created apparatus has a great degree of visibility and provides method of calculations brought to automatism. With its help in a large number were solved a variety of problems that are not available with other approaches. The works of Soviet physicists, in turn, had an impact on the work of R. Feynman and J. Schwinger in such areas as the theory of superfluidity, the polaron problem, the Casimir effect. Discussion. The quantum-field theory of many bodies that has been created has decisively contributed to the rapid development of the physics of condensed matter in the next decades, and until now remains the most powerful and effective tool for theoretical research in this field. Here the contribution of Soviet physicists can not be overestimated.

Reference: 
  1. Bell E.T. Men of Mathematics. Vol. 1. London: Penguin books, 1953. 323 p.
  2. Interview with Igor E. Dzyloshinskii // Physics of Scale Activities, 14–15 December, 2001. Irvine, California. Рр. 1–41.
  3. Arseev P.I. On the nonequilibrium diagram technique: Derivation, some features and applications. Phys. Usp., 2015, Vol. 58, no. 12, pp. 1159–1205.
  4. Keldysh L.V. Real-time nonequilibrium Green’s functions // Proc. of conf. «Progress in Nonequilibrium Green’s Functions», Dresden, Germany, 19–22, August 2002. Рр. 4–17.
  5. Abrikosov A.A. My years with Landau // Physics today. 1973. January. Pp. 55–60.
  6. Ginzburg V.L. About Science, Myself and Others. Bristol, IOP Publishing Ltd., 2005, 360 p.
  7. Kirzhnits D.A. Field Methods of the Theory of Many Particles. Moscow, State Atom, 1963, 344 p. (In Russian). 
  8. Abrikosov A.A., Gor’kov L.P., Dzyaloshinskii I.E. Quantum Field Theory in Statistical Physics. Moscow, Fizmatlit, 1962, 443 p. (in Russian). 
  9. Okun’ L.B. I.Ya. Pomeranchuk – how I knew him. In: Recollections about I.Ya. Pomeranchuk, Moscow, Nauka, 1988, pp. 125–131 (in Russian).
  10. Ioffe B.L. The first years of communication with I.Ya. Pomeranchuk. In: Recollections about I.Ya. Pomeranchuk. Moscow, Nauka, 1988, pp. 88–94 (in Russian). 
  11. Galanin A.D. About the first years of work in the ITEP with I.Ya. Pomeranchuk. In; Recollections about I.Ya. Pomeranchuk. Moscow, Nauka, 1988, pp. 69–70 (in Russian).
  12. Ioffe B.L. Without Retouching: Portraits of Physicists on the Background of the Era, Moscow, Fazis, 2004, 160 p. (in Russian). 
  13. Abrikosov A.A. Story about the temperature technique Proc. of conf. «Progress in Nonequilibrium Green’s Functions», Dresden, Germany, 19–22 August 2002. Рр. 2–3.
  14. Smorodinsky Ya.A. The displacement of terms of hydrogen-like atoms and the anomalous magnetic moment of an electron. Phys. Usp., 1949, vol. 39, no. 3, pp. 325–358 (in Russian).
  15. Feynman R.P. Relativistic cut-off for quantum electrodynamics Phys. Rev. 1948. Vol. 74, No. 10. Pp. 1430–1438.
  16. Feynman R.P. Space-time approach to quantum electrodynamics Phys. Rev. 1949. Vol. 76, No. 6. Pp. 769–789.
  17. Berestetskii V.B. Perturbation theory in quantum electrodynamics. Phys. Usp., 1952, vol. 46, no. 2, pp. 231–278 (in Russian). 
  18. Ioffe B.L. Something from the history of the atomic project in the USSR. Siberian Physical Journal, 1995, no. 2, pp. 67–87 (in Russian).
  19. Galanin A.D. Radiative corrections in quantum electrodynamics. Reports of the Academy of Sciences of the USSR, 1951, vol. 79, pp. 229–232 (in Russian).
  20. Ioffe B.L. The first dozen years of the history of ITEP Theoretical Physics Laboratory. arXiv: 1208.1386v1[physics.hist-ph] 7 Aug 2012.
  21. Ioffe B.L. Landau’s theoretical minimum, Landau’s seminar, ITEP in the beginning of the 1950’s. arXiv: hep-ph/0204295v1 25 Apr2002.
  22. Wentzel G. Quantum Theory of Fields (until 1947). Theoretical Physics in the Twentieth Century. New York: Interscience Publishers, 1960. Pp. 48–77. 
  23. Mehra J., Rechenberg H. The historical development of quantum theory. Vol. 6. Part 2. New York: Springer–Verlag, 2001. Рр. 671–1612.
  24. Berestetskii V.B. Zero-charge and asymptotic freedom. Phys. Usp., 1976, vol. 19, no. 3, pp. 934–943.
  25. The letters of Richard Feynman. New York: Basic books, 2005. 486 р.
  26. Abrikosov A.A., Landau L.D., Khalatnikov I.M. The removal of infinities in quantum electrodynamics. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 607–620.
  27. Abrikosov A.A., Landau L.D., Khalatnikov I.M. An asymptotic expression for the electron Green function in quantum electrodynamics. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 611–615.
  28. Abrikosov A.A., Landau L.D., Khalatnikov I.M. An asymptotic expression for the photon Green’s function in quantum electrodynamics. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 616–620.
  29. Abrikosov A.A., Landau L.D., Khalatnikov I.M. The electron mass in quantum electrodynamics. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 621–625.
  30. Khalatnikov I.M. Dau, Centaur and Others. Moscow, Fizmatlit, 2008, 192 p. (in Russian).
  31. Dzyaloshinskii I.E. Landau through a pupil’s eyes. In: LANDAU, The Physicist and the Man, Oxford, Pergamon Press, 1989, pp. 89–96.
  32. Landau L.D., Pomeranchuk I.Ya. On Point Interaction in Quantum Electrodynamics. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 654–658. 
  33. Fradkin E.S. The asymptote of Green’s function in quantum electrodynamics. JETP, 1955, vol. 1, no. 3, pp. 604–606.
  34. Brodsky S., Drell S.D. The present status of quantum electrodynamics. Annual Rev. of Nuclear Sc., 1970, vol. 20, Palo Alto, California, pp. 147–194. 
  35. Mehra J., Milton K.A. Climbing the Mountain. Oxford: Oxford Univ. Press, 2000. 695 р.
  36. Green G. An essay on the application of mathematical analyzes to the theories of electricity and magnetism. In: Mathematical Papers of the Late George Green. London: Macmillan and CO., 1871. Pp. 1–82.
  37. Green G. On the propagation of light in crystallized media. In: Mathematical Papers of the Late George Green. London: Macmillan and CO., 1871. Pp. 291–311.
  38. Schwinger J. On gauge invariance and vacuum polarization Phys. Rev. 1951. Vol. 82. Pр. 664–679.
  39. Schwinger J. The theory of quantized fields. I. Phys. Rev. 1951. Vol. 82. Pр. 914–927.
  40. Schwinger J. On the Green’s functions on quantized fields. I, II. Proc. Nat. Acad. Sci. (USA). 1951. Vol. 37. Pр. 452–455, 455–459.
  41. Feynman R.P. The theory of positrons. Phys. Rev. 1949. Vol. 76, no. 6. Pр. 749–759.
  42. Bonch-Bruevich V.L. The Fermi distribution at absolute zero, taking into account the inter-action of electrons with zero point vibrations of the lattice. JETP, 1955, vol. 1, no. 1 pp. 169–170.
  43. Migdal A.B. Interaction between electrons and lattice vibrations in a normal metal. JETP, 1958, vol. 7, no. 6, pp. 996–1001.
  44. Bardeen J. Electron-Phonon Interaction and Superconductivity. Physics 1971–1980. Singapore, World Scientific Publishing Co., 1992, pp. 56–69.
  45. Frolich H. Interaction of electrons with lattice vibrations. Proc. Roy. Soc (London), 1952, vol. A215, pр. 291–298.
  46. Recollections about Academician A.B. Migdal. Moscow, Fizmatlit, 2003, 256 pp. (in Russian).
  47. Galitskii V.M., Migdal A.B. Application quantum field theory methods to the many body problem. JETP, 1958, vol. 7, no. 1, pp. 96–104.
  48. Galitskii V.M. The energy spectrum of a non-ideal Fermi gas. JETP, 1958, vol. 7, no. 1, pp. 104–112.
  49. Beliaev S.T. Application of the methods of quantum field theory to a system of bosons. JETP, 1958, vol. 7, no. 2, pp. 289–298.
  50. Beliaev S.T. Energy spectrum of a non-ideal Bose gas. JETP, 1958, vol. 7, no. 2, pp. 299–307.
  51. Gor’kov L.P. On the energy spectrum of superconductors. JETP, 1958, vol. 7, no. 3, pp. 505–508.
  52. Landau L.D. The properties of the Green function for particles in statistics. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 749– 751.
  53. Migdal A.B. The momentum distribution of interacting Fermi particles. JETP, 1957, vol. 5, no. 2, pp. 333–334.
  54. Landau L.D. The theory of the Fermi liquid. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 723–730.
  55. Landau L.D. The theory of the Fermi liquid. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 752–760.
  56. Landau L.D. Statistical Physics. Oxford, Pergamon Press, 1980, 562 p.
  57. Matsubara T. A new approach to quantum-statistical mechanics. Progr. Theor. Phys., 1955, vol. 14, no. 4, pp. 351–378.
  58. Coleman P. Introduction to Many-Body Physics. Cambridge, Cambridge Univ. Press, 2015, 798 p.
  59. Abrikosov A.A., Gor’kov L.P., Dzyaloshinskii I.E. On the application of quantum-fieldtheory methods to problems of quantum statistics at finite temperatures. JETP, 1959, vol. 9, no. 3, pp. 636–641.
  60. Fradkin E.S. The Green’s functions methods in quantum statistics. JETP, 1959, vol. 9, no. 4, pp. 912–919.
  61. Bogolyubov N.N, Tyablikov S.V. Leading and retarded Green functions in statistical physics. Reports of the Academy of Sciences of the USSR, 1959, vol. 126, no. 1, pp. 53–56 (in Russian).
  62. Gor’kov L.P. Microscopic derivation of the Ginzburg–Landau equations in the theory of superconductivity. JETP, 1959, vol. 9, no. 6, pp. 1364–1367.
  63. Gor’kov L.P. Developing BCS ideas in the former Soviet Union. BCS: 50 Years, ed. L. Cooper and D. Feldman, Singapore, World Sci., 2011, pp. 107–126.
  64. Cooper L. Bound electron pairs in a degenerate Fermi gas. Phys. Rev., 1956, vol. 104, no. 4, pр. 1189–1190.
  65. Bardeen J., Cooper L.N., Schrieffer J.R. Microscopic theory of superconductivity. Phys. Rev., 1957, vol. 106, pp. 162–164.
  66. Beliaev S.T. Remembering AB. In: Recollections about Academician A.B. Migdal. Moscow, Fizmatlit, 2003, pp. 14–18 (in Russian).
  67. Nambu Y. Quasi-particles and gauge invariance in the theory of superconductivity. Phys. Rev., 1960, vol. 117, no. 3, pp. 648–663.
  68. Martin P.C., Schwinger J. Theory of many-particle systems. Phys. Rev., 1959, vol. 115, pр. 1342–1373.
  69. Pines D. The Many-Body Problem. New York, W.A. Benjamin, Inc., 1961, 456 p.
  70. Schrieffer R. Theory of Superconductivity. New York, W.A. Benjamin, Inc., 1964, 332 p.
  71. Zubarev D.N. Double-time Green functions in statistical physics. Phys. Usp., 1960, vol. 3, pp. 320–345.
  72. Alekseev A.I. The application of the methods of quantum field theory in statistical physics. Phys. Usp., 1961, vol. 4, pp. 23–50.
  73. Bonch-Bruevich V.L., Tyablikov S.V. The Green Function Method in Statistical Mechanics. Amsterdam, North-Holland, 1962, 251 p.
  74. Abrikosov A.A., Gor’kov L.P., Dzyaloshinskii I.E. Quantum Field Theory in Statistical Physics. Oxford, Pergamon Press, 1963, 366 р.
  75. Tsvelik A.M. Quantum Field Theory in Condensed Matter Physics. Cambridge, Cambridge Univ. Press, 1995, 360 p.
  76. Kubo R. Statistical-mechanical theory of irreversible processes. J. Phys. Soc. Jpn., 1957, vol. 12, pp. 570–586.
  77. Zubarev D.N. Nonequilibrium Statistical Thermodynamics. New York, Springer, 1995, 489 p.
  78. Schwinger J. Brownian motion of a quantum oscillator. Math. Phys., 1961, vol. 2, no. 3, pр. 407–432. 
  79. Kadanov L.P., Baym G. Quantum Statistical Mechanics. New York, W.A. Benjamin, Inc., 1962, 203 p.
  80. Konstantinov O.V., Perel V.I. A diagram technique for evaluating transport quantities. JETP, 1961, vol. 12, no. 1, pp. 142–149.
  81. Keldysh L.V. Diagram technique for nonequilibrium processes. JETP, 1965, vol. 20, no. 4, pp. 1018–1026.
  82. Mehra J. The Beat of a Different Drum. Oxford, Clarendon Press, 1994, 637 p.
  83. Feynman R.P. Atomic theory of the λ transition in liquid helium. Phys. Rev., 1953, vol. 91, no. 6, pр. 1291–1301.
  84. Feynman R.P. Atomic theory of liquid helium near absolute zero. Phys. Rev., 1953, vol. 91, no. 6, pр. 1301–1308.
  85. Feynman R.P. Atomic theory of the two-fluid model of liquid helium. Phys. Rev., 1954, vol. 94, no. 2, pр. 262–277.
  86. Feynman R.P., Cohen M. Energy spectrum of the excitations in liquid helium. Phys. Rev., 1956, vol. 102, no. 5, pр. 1189–1204.
  87. Cohen M., Feynman R.P. Theory of inelastic scattering of cold neutrons from liquid helium. Phys. Rev., 1957, vol. 107, no. 1, pр. 14–24.
  88. Andronikashvili E.L. Reflections on Liquid Helium. New York, Amer. Inst. of Physics, 1990. 328 p.
  89. Osborn D.V. The rotation of liquid helium II. Proc. Phys. Soc., 1950, sec. A, vol. 63, no. 8, pp. 909–912.
  90. Landau L.D., Lifshitz E.M. On the Rotation of Liquid Helium. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 650–653.
  91. Feynman R.P. Application of quantum mechanics to liquid helium. Progr. in Low Temp. Phys., 1955, vol. 1, pр. 17–53.
  92. London F. Superfluids. Vol. II. New York, Dover Publications, Inc., 1964, 217 p.
  93. Landau L.D. Collected Papers. Vol. 2. Moscow, Nauka, 1969, 451 p. (in Russian).
  94. Collected Papers of L.D. Landau. New York, Gordon and Breach, Sci. Publishers, 1965, 836 p.
  95. Volovik G.E. Superfluids in rotation: Landau–Lifshitz vortex sheets vs Onsager–Feynman vortices. Phys. Usp., 2015, vol. 58, no. 9, pp. 970–979
  96. Abrikosov A.A. On the magnetic properties of superconductors of the second group. JETP, 1957, vol. 5, no. 6, pp. 1174–1182.
  97. Ginzburg V.L. A Remarkable Physicist. Further thoughts. In: LANDAU, The Physicist and the Man, Oxford, Pergamon Press, 1989, pp. 117–135.
  98. Rumer Yu.B. A Page or Two of Reminiscences about L.D. Landau. In: LANDAU, The Physicist and the Man. Oxford, Pergamon Press, 1989, pp. 208–213.
  99. Abrikosov A.A. Recollections of L.D. Landau. In: LANDAU, The Physicist and the Man, Oxford, Pergamon Press, 1989, pp. 29–35.
  100. Feinberg E.B. Landau and others. In: LANDAU, The Physicist and the Man, Oxford, Pergamon Press, 1989, pp. 105–116.
  101. Landau L.D. Electron Motion in the Crystal Lattices. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 67–68.
  102. Frenkel Ya.I. On the absorption of light and the trapping of electrons and positive holes in crystalline dielectrics. Phys. Zeitschrift der Sovjet Union, 1936, vol. 9, pp. 158–186.
  103. Pekar S.I. Localized quantum states of an electron in an ideal ion crystal. JETP, 1946, vol. 16, no. 4, pp. 341–348 (in Russian).
  104. Landau L.D., Pekar S.I. The Effective Mass of the Polaron. In: Coll. Papers of L.D. Landau, New York, Gordon and Breach, Sci. Publishers, 1965, pp. 478–483.
  105. Pekar S.I. Untersuchengen uber die Elektronentheorie der Kristalle. Berlin, Akademie–Verlag, 1954, 184 s.
  106. Frolich H. Electrons in lattice fields. Adv. Phys., 1954, vol. 3, no. 11, pр. 325–361.
  107. Feynman R.P. Slow electrons in a polar crystal. Phys. Rev., 1955, vol. 97, no. 3, pр. 660–665.
  108. Feynman R.P., Hellerwarth R.W., Iddings C.K., Platzman P.M. Mobility of slow electrons in a polar crystal. Phys. Rev., 1962, vol. 127, no. 4, pр. 1004–1017.
  109. Mostepanenko V.M., Trunov N.Ya. The Casimir effect and its applications. Phys. Usp., 1988, vol. 31, pp. 965–987.
  110. Lifshitz E.M. Theory of Molecular Attraction Forces between Condensed Bodies. Perspectives in Theoretical Physics: The Collected Papers of E.M. Lifshitz. Oxford, Pergamon Press, 1992, pp. 313–317.
  111. Lifshitz E.M. The Theory of Molecular Attractive Forces between Solids. Perspectives in Theoretical Physics: The Collected Papers of E.M. Lifshitz. Oxford, Pergamon Press, 1992, pp. 329–349.
  112. Zeldovich Ya.B. Recollections of the Teacher. In: LANDAU, The Physicist and the Man. Oxford, Pergamon Press, 1989, pp. 257–262.
  113. Ioffe B.L. If Landau were AliveNow. In: LANDAU, The Physicist and the Man. Oxford, Pergamon Press, 1989, pp. 153–156.
  114. Leighton R. Forty-five Snowy I. Engineering and Science. Summer, 1991, pр. 31–39.
  115. Leighton R. Tuva or Bust! New York, W.W. Norton and Co., 2000, 262 р.
  116. Vainstein S. Nomads of South Siberia: The Pastoral Economies of Tuva. Cambridge, Cambridge Univ. Press, 1980, 290 p.
  117. Tishkov V.A. Reflections on the results of life: A conversation with Sevyan Izrailevich Weinstein. Ethnographic Review, 2008, № 2, pp. 70–86 (in Russian).
Received: 
29.05.2018
Accepted: 
14.09.2018
Published: 
31.10.2018
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