RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1988

 / 

February

←  →

Methodological notes


Quantization of the electromagnetic field


V.A. Fock Institute of Physics, St. Petersburg State University, ul. Ulyanovskaya 1, Petrodvorets, St. Petersburg, 198904, Russian Federation

The question of a canonical quantization of the electromagnetic field as a system with two primary constraints is analyzed. Attention is focused on the following aspects of the problem: 1) the conditions on physical states; 2) the ``old'' and ``new'' Gupta formalisms; 3) the interpretation of the operators $\hat\alpha_0$, $\hat\alpha_0^+$; 4) the vacuum in quantum electrodynamics. The starting point for the analysis is Dirac's quantization recipe for systems with constraints. It is shown that the Fermi formalism with a condition on the physical states is completely correct.

Fulltext pdf (458 KB)
Fulltext is also available at DOI: 10.1070/PU1988v031n02ABEH005699
PACS: 12.20.Ds, 11.10.Ef (all)
DOI: 10.1070/PU1988v031n02ABEH005699
URL: https://ufn.ru/en/articles/1988/2/d/
Citation: Prokhorov L V "Quantization of the electromagnetic field" Sov. Phys. Usp. 31 151–162 (1988)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Прохоров Л В «Квантование электромагнитного поля» УФН 154 299–320 (1988); DOI: 10.3367/UFNr.0154.198802f.0299

References (41) ↓ Cited by (10) Similar articles (20)

  1. P. A. M. Dirac Proc. R. Soc. London, Ser A. 114 243 (1927)
  2. N. N. Bogolyubov and D. V. Shirkov Introduction To The Theory Of Quantized Fields 2nded. (Wiley, N.Y., 1979); Russ. original, N. N. Bogolyubov and D. V. Shirkov Introduction To The Theory Of Quantized Fields 4th Edition (Nauka, M., 1985)
  3. E. Fermi Rend. Accad. Lincei 9 881 (1929), [Russ. transl., in Ref. 6]
  4. E. Fermi Rend. Accad. Lincei. 12 431 (1930), [Russ. transl., in Ref. 6]
  5. E. Fermi Rev. Mod. Phys. 4 87 (1932), [Russ. transl., in Ref. 6]
  6. E. Fermi Scientific Works (Russ. transl., Nauka, M., 1971)
  7. W. Heisenberg and W. Pauli Z. Phys. 59 168 (1930), [Russ. transl., in Ref. 38]
  8. P.A. M. Dirac Principles Of Quantum Mechanics (Oxford Univ. Press, London, 1958); Russ. transl., P.A. M. Dirac Principles Of Quantum Mechanics (Fizmatgiz, M., 1960); P.A. M. Dirac Principles Of Quantum Mechanics (Nauka, M., 1979) p. 1974
  9. P. A. M. Dirac Lectures In Quantum Field Theory (Academic Press, N.Y., 1966); Russ. transl., P. A. M. Dirac Lectures In Quantum Field Theory (Mir, M., 1971)
  10. S. T. Ma Phys. Rev. 75 535 (1949)
  11. F. J. Belinfante Phys. Rev. 76 226 (1949)
  12. W. Pauli Lectures On Physics Vol. Vol. 6 (The MIT Press, Cambridge, MA, 1973)
  13. S. N. Gupta Proc. Phys. Soc. London, Ser. A 63 681 (1950)
  14. I. V. Polubarinov ""Equations of quantum electrodynamics" (in Russian)" Preprint R-2421 (Joint Institute for Nuclear Research, Dubna, 1965)
  15. K. Bleuler Helv. Phys. Acta. 23 567 (1950)
  16. S. N. Gupta Can. J. Phys. 35 961 (1957)
  17. S. Sunakawa Prog. Theor. Phys. 19 221 (1958)
  18. S. N. Gupta Prog. Theor. Phys. 21 581 (1959)
  19. S. S. Schweber An Introduction To Relativistic Quantum Field Theory (Row, Peterson, Evanston, Ill., 1961); Russ. transl., S. S. Schweber An Introduction To Relativistic Quantum Field Theory (IL, M., 1963)
  20. A. I. Akhiezer and V. B. Berestetski&ibreve; Quantum Electrodynamics (Interscience, N.Y., 1965); Russ. original, A. I. Akhiezer and V. B. Berestetski&ibreve; Quantum Electrodynamics 3rd Edition (Nauka, M., 1969)
  21. J. M. Jauch and F. Rohrlich The Theory Of Photons And Electrons (Heidelberg, Berlin); J. M. Jauch and F. Rohrlich The Theory Of Photons And Electrons (Springer-Verlag, N. Y., 1980)
  22. P. A. M. Dirac Can. J. Math. 2 129 (1950)
  23. P. A. M. Dirac Proc. R. Soc. London, Ser. A: 246 326 (1958)
  24. P. A. M. Dirac Lectures In Quantum Mechanics (Academic Press, N. Y., 1964); Russ. transl., P. A. M. Dirac Lectures In Quantum Mechanics (Mir, M., 1968)
  25. E. Noether Variational Principles Of Mechanics (Russ. transl., IL, M., 1959)
  26. L. V. Prokhorov Yad. Fiz. 35 229 (1982); L. V. Prokhorov Sov. J. Nucl. Phys. 35 129 (1982)
  27. L. V. Prokhorov Fiz. Elem. Chastits At. Yadra 13 1094 (1982); L. V. Prokhorov Sov. J. Part. Nucl. 13 456 (1982)
  28. W. Heisenberg and W. Pauli Z. Phys. 56 1 (1929), [Russ. transl., in Ref. 38]
  29. J. Schwinger Phys. Rev. 74 1439 (1948)
  30. S. N. Gupta Proc. Phys. Soc. Ser. A. 64 850 (1951)
  31. Ning Hu Phys. Rev. 76 391 (1949)
  32. I. M. Gel’fand and N. Ya. Vilenkin Some Applications Of Harmonic Analysis. Rigged Hilbert Spaces (in Russian) (Fizmatgiz, M., 1961)
  33. G. Konisi and T. Ogimoto Prog. Theor. Phys. 20 868 (1958); G. Konisi and T. Ogimoto Ibid 21 727 (1959)
  34. K. Nad’ Spaces Of States With An Indefinite Metric In Quantum Field Theory [Russ. Transl. (Mir, M.,]., 1969)
  35. T. Kugo and I. Ojima Prog. Theor. Phys. Suppl. No. 66 1 (1979)
  36. P. Senjanovic Ann. Phys. (N.Y.) 100 227 (1976)
  37. P. Jordan and W. Pauli Z. Phys. 47 151 (1928), [Russ. transl., in Ref. 38]
  38. W. Pauli Works On Quantum Theory Vol. Vol. 2 (1977); Russ. transl., W. Pauli Works On Quantum Theory (Nauka M., 1977)
  39. V. Fock Phys. Z. Sowjetunion 6 425 (1934), [Russ. transl., in Ref. 40]
  40. V. A. Fok Works In Quantum Field Theory (in Russian) (Izd. Leningr. univ., L., 1957)
  41. P. A. M. Dirac The Principles Of Quantum Mechanics (3rd edition, Clarendon Press, Oxford, 1947)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions