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Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media


Peter the Great Saint-Petersburg Polytechnic University, ul. Polytechnicheskaya 29, St. Petersburg, 195251, Russian Federation

Applying a quantum-mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy—momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham's symmetric energy-momentum tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular moment (spin) of an electromagnetic field in the medium. Only the Minkowski tensor enables experimentally confirmed multiple-of-ħ spin values, providing the grounds for choosing the Minkowski representation as the adequate form for the momentum density of a transverse electromagnetic field in a transparent medium, whether the field is treated classically or quantum mechanically. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasi-static and static fields.

Fulltext is available at IOP
Keywords: the Minkowski energy—momentum tensor, quantum theory, radiation phenomena, spin and mass of a photon in matter
PACS: 12.20.−m, 41.20.Jb, 41.60.Bq (all)
DOI: 10.3367/UFNe.2017.04.038138
URL: https://ufn.ru/en/articles/2017/9/f/
Citation: Toptygin I N "Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media" Phys. Usp. 60 935–947 (2017)
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Received: 21st, June 2016, revised: 8th, April 2017, 12th, April 2017

Оригинал: Топтыгин И Н «Квантовое описание поля в макроскопической электродинамике и свойства фотонов в прозрачных средах» УФН 187 1007–1020 (2017); DOI: 10.3367/UFNr.2017.04.038138

References (62) ↓ Cited by (3) Similar articles (20)

  1. Tamm I E Osnovy Teorii Elektrichestva (M.: Nauka, 1976); Per. na angl. yaz., Tamm I E Fundamentals Of The Theory Of Electricity (Moscow: Mir Publ., 1979)
  2. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Nauka, 1982); Per. na angl. yaz., Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  3. Jackson J D Classical Electrodynamics (New York: John Wiley and Sons, 1999)
  4. Ryazanov M I Elektrodinamika Kondensirovannogo Veshchestva (M.: Nauka, 1984)
  5. Pamyatnykh E A, Turov E A Osnovy Elektrodinamiki Material’nykh Sred v Peremennykh i Neodnorodnykh Polyakh (M.: Fizmatlit, 2000)
  6. Ginzburg V L Zh. Eksp. Teor. Fiz. 10 589 (1940)
  7. Minkowski H "Die Grundlagen für die elektromagnetischen Vorgënge in bewegten Körpern" Nachr. König. Ges. Wiss. Göttingen, Math.-Phys. Kl. 53 (1908); Per. na russk. yaz., Minkovskii G Einshteinovskii Sbornik 1978 - 1979 (Pod red. V L Ginzburga) (M.: Nauka, 1983) p. 5
  8. Minkowski H "Eine Ableitung der Grundgleichungen für die elektromagnetishen Forgänge in bewegten Körpern fom Standpunkt der Elektronentheorie" Math. Ann. 68 526 (1902); Per. na russk. yaz., Minkovskii G "Vyvod osnovnykh uravnenii dlya elektromagnitnykh protsessov v dvizhushchikhsya telakh s tochki zreniya teorii elektronov" Einshteinovskii Sbornik 1978 - 1979 (Pod red. V L Ginzburga) (M.: Nauka, 1983) p. 64
  9. Abraham M Rend. Circ. Mat. Palermo 28 1 (1909); Abraham M Rend. Circ. Mat. Palermo 31 527 (1910)
  10. Pauli W Relativitätstheorie (Encyklopädie Der Mathematischen Wissenschaften, Bd. V, Tl. 2, Heft IV) (Leipzig: Teubner, 1921); Per. na angl. yaz., Pauli W Theory Of Relativity (New York: Pergamon Press, 1958); Per. na russk. yaz., Pauli V Teoriya Otnositel’nosti (M.: Gostekhizdat, 1947)
  11. Ginzburg V L Teoreticheskaya Fizika i Astrofizika. Dopolnitel’nye Glavy 3-e izd. (M.: Nauka, 1987); Per. na angl. yaz., Ginzburg V L Applications Of Electrodynamics In Theoretical Physics And Astrophysics 2nd ed. (New York: Gordon and Breach Sci. Publ., 1989)
  12. Ugarov V A Spetsial’naya Teoriya Otnositel’nosti (M.: Nauka, 1977)
  13. Toptygin I N Sovremennaya Elektrodinamika Ch. 2 Teoriya Elektromagnitnykh Yavlenii v Veshchestve (M. - Izhevsk: In-t komp’yut. issled. RKhD, 2005); Dopolnennyi perevod na angl. yaz., Toptygin I N Electromagnetic Phenomena In Matter. Statistical And Quantum Approaches (Weinheim: Wiley-VCH, 2015)
  14. Skobel’tsyn D V Usp. Fiz. Nauk 110 253 (1973); Skobel’tsyn D V Sov. Phys. Usp. 16 381 (1973)
  15. Ginzburg V L Usp. Fiz. Nauk 110 309 (1973); Ginzburg V L Sov. Phys. Usp. 16 381 (1973)
  16. Ginzburg V L, Ugarov V A Usp. Fiz. Nauk 118 175 (1976); Ginzburg V L, Ugarov V A Sov. Phys. Usp. 19 94 (1976)
  17. Toptygin I N, Levina K Usp. Fiz. Nauk 186 146 (2016); Toptygin I N, Levina K Phys. Usp. 59 141 (2016)
  18. Landau L D, Lifshits E M Teoriya Polya (M.: Nauka, 1973); Per. na angl. yaz., Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Butterworth-Heinemann, 2000)
  19. Bolotovskii B M, Stolyarov S N Usp. Fiz. Nauk 114 569 (1974); Bolotovskii B M, Stolyarov S N Sov. Phys. Usp. 18 875 (1975)
  20. Huttner B, Barnett S M Phys. Rev. A 46 4306 (1992)
  21. Philbin T G New J. Phys. 12 123008 (2012)
  22. Horsley S A R Phys. Rev. A 86 023830 (2012)
  23. Horsley S A R, Philbin T G New J. Phys. 16 013030 (2014)
  24. Goldstein H Classical Mechanics (Reading, Mass.: Addison-Wisley, 1950)
  25. Heitler W The Quantum Theory Of Radiation (Oxford: Clarendon Press, 1954); Per. na russk. yaz., Gaitler V Kvantovaya Teoriya Izlucheniya (M.: IL, 1956)
  26. Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika (M.: Gostekhizdat, 1953); Per. na angl. yaz., Akhiezer A I, Berestetskii V B Elements Of Quantum Electrodynamics (London: Oldbourne Press, 1962); Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika 2-e izd. (M.: Fizmatgiz, 1959); Per. na angl. yaz., Akhiezer A I, Berestetskii V B Quantum Electrodynamics (New York: Interscience Publ., 1965); Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika 3-e izd. (M.: Nauka, 1969); Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika 4-e izd. (M.: Nauka, 1981)
  27. Kompaneets A S Teoreticheskaya Fizika (M.: GITTL, 1957); Per. na angl. yaz., Kompaneyets A S Theoretical Physics (Moscow: Mir Publ., 1965)
  28. McConnell J Quantum Particle Dynamics (Amsterdam: North-Holland, 1960)
  29. Berestetskii V B, Lifshits E M, Pitaevskii L P Kvantovaya Elektrodinamika (M.: Nauka, 1989); Per. na angl. yaz., Berestetskii V B, Lifshitz E M, Pitaevskii L P Quantum Electrodynamics (Oxford: Butterworth-Heinemann, 1999)
  30. Mandel L, Wolf E Optical Coherence And Quantum Optics (Cambridge: Cambridge Univ. Press, 1995); Per. na russk. yaz., Mandel’ L, Vol’f E Opticheskaya Kogerentnost’ i Kvantovaya Optika (M.: Fizmatlit, 2000)
  31. Bjorken D, Drell D Relativistic Quantum Field (New York: McGraw-Hill, 1976); Per. na russk. yaz., B’erken Dzh D, Drell S D Relyativistskaya Kvantovaya Teoriya T. 2 Relyativistskie Kvantovye Polya (M.: Nauka, 1978)
  32. Dirac P A M The Principles Of Quantum Mechanics (Oxford: Clarendon Press, 1958); Per. na russk. yaz., Dirak P A M Printsipy Kvantovoi Mekhaniki (M.: Fizmatgiz, 1960)
  33. Ehrenfest P Z. Phys. 45 455 (1927)
  34. Glauber R Coherence and Quantum Detection in Quantum Optics (Proc. of the Intern. School of Physics Enrico Fermi, Course XVII, Ed. R Glauber) (New York: Academic Press, 1969); Per. na russk. yaz., Glauber R (Red.) Kogerentnye Sostoyaniya v Kvantovoi Teorii Sbornik Statei (M.: Mir, 1972)
  35. Loudon R The Quantum Theory Of Light (Oxford: Clarendon Press, 1973); Per. na russk. yaz., Loudon R Kvantovaya Teoriya Sveta (M.: Mir, 1973)
  36. Scully M O, Zubairy M S Quantum Optics (Cambridge: Cambridge Univ. Press, 1997); Per. na russk. yaz., Skalli M O, Zubairi M S Kvantovaya Optika (M.: Fizmatlit, 2002)
  37. Toptygin I N Foundations Of Classical And Quantum Electrodynamics (New York: Wiley-VCH, 2014)
  38. Cherenkov P A Dokl. Akad. Nauk SSSR 2 451 (1934); Cherenkov P A C.R. Acad. Sci. USSR 2 451 (1934); Cherenkov P A Usp. Fiz. Nauk 93 385 (1967)
  39. Vavilov S N Dokl. Akad. Nauk SSSR 2 457 (1934); Vavilov S I C.R. Acad. Sci. USSR 2 457 (1934); Vavilov S I Usp. Fiz. Nauk 93 383 (1967)
  40. Tamm I E, Frank I M Dokl. Akad. Nauk SSSR 14 107 (1937); Tamm I E, Frank I M C.R. Acad. Sci. USSR 14 107 (1937); Tamm I E, Frank I M Usp. Fiz. Nauk 93 388 (1967)
  41. Tamm I E, Frank I M Trudy FIAN 2 (4) 63 (1944)
  42. Frank I M Izluchenie Vavilova—Cherenkova. Voprosy Teorii (M.: Nauka, 1988)
  43. Sokolov A A, Ternov I M Relyativistskii Elektron (M.: Nauka, 1983); Per. na angl. yaz., Sokolov A A, Ternov I M Radiation From Relativistic Electrons (New York: American Institute of Physics, 1986)
  44. Ryazanov M I Zh. Eksp. Teor. Fiz. 45 333 (1963); Ryazanov M I Sov. Phys. JETP 18 232 (1964)
  45. Gailitis A, Tsytovich V N Zh. Eksp. Teor. Fiz. 46 1726 (1964); Gailitis A, Tsytovich V N Sov. Phys. JETP 19 1165 (1964)
  46. Batygin V V Zh. Eksp. Teor. Fiz. 53 890 (1967); Batygin V V Sov. Phys. JETP 26 540 (1968)
  47. Ginzburg V L, Frank I M Zh. Eksp. Teor. Fiz. 16 15 (1946); Ginzburg V L, Frank I M J. Phys. USSR 9 353 (1945)
  48. Ginzburg V L, Tsytovich V N Perekhodnoe Izluchenie i Perekhodnoe Rasseyanie : Nekotorye Voprosy Teorii (M.: Nauka, 1984); Per. na angl. yaz., Ginzburg V L, Tsytovich V N Transition Radiation And Transition Scattering (Bristol: A. Hilger, 1990)
  49. Okun’ L B Usp. Fiz. Nauk 158 511 (1989); Okun’ L B Sov. Phys. Usp. 32 629 (1989)
  50. Okun’ L B Usp. Fiz. Nauk 170 1366 (2000); Okun L B Phys. Usp. 43 1270 (2000)
  51. Okun’ L B Usp. Fiz. Nauk 178 541 (2008); Okun L B Phys. Usp. 51 513 (2008); Okun’ L B Usp. Fiz. Nauk 178 653 (2008); Okun L B Phys. Usp. 51 622 (2008)
  52. Moskalev A N Relyativistskaya Teoriya Polya (SPb.: PIYaF RAN, 2006)
  53. Chefranov S G Zh. Eksp. Teor. Fiz. 150 18 (2016); Chefranov S G JETP 123 12 (2016)
  54. Chefranov S G Zh. Eksp. Teor. Fiz. 126 333 (2004); Chefranov S G JETP 99 296 (2004)
  55. Ginzburg V L Usp. Fiz. Nauk 166 1033 (1996); Ginzburg V L Phys. Usp. 39 973 (1996)
  56. Barnett S M Phys. Rev. Lett. 104 070401 (2010)
  57. Philbin P G Phys. Rev. A 83 013823 (2011)
  58. Pfeifer R N C et al. Rev. Mod. Phys. 79 1197 (2007)
  59. Kemp B A J. Appl. Phys. 109 111101 (2011)
  60. Ramos T, Rubilar G F, Obukhov Y N J. Opt. 17 025611 (2015)
  61. Pitaevskii L P Zh. Eksp. Teor. Fiz. 39 1450 (1960); Pitaevskii L P Sov. Phys. JETP 12 1008 (1961)
  62. Polevoi V G, Rytov S M Usp. Fiz. Nauk 125 549 (1978); Polevoi V G, Rytov S M Sov. Phys. Usp. 21 630 (1978)

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