Skip to main content
SpringerLink
Log in

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock–Schwinger (FS) gauge for the Abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev–Popov ghosts-free non-Abelian gauge theories. This method is expected to be applicable to non-Abelian gauge theories including supersymmetric ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abers, E. S. and Lee, B. W. (1973). Physical Report C 9, 1.

    Google Scholar 

  • Banerjee, R. (2000). Physics Letters B 488, 27.

    CAS  MathSciNet  Google Scholar 

  • Becchi, C., Rouet, A., and Stora, R. (1975). Communications in Mathematical Physics 42, 127.

    Google Scholar 

  • Bialynicki-Birula, I. (1968). Physical Review 166, 1505.

    Google Scholar 

  • Durand, L. and Mendel, E. (1982). Physical Review D 26, 1368.

    Google Scholar 

  • Faddeev, L. D. and Jackiw, R. (1988). Physical Review Letters 60, 1692.

    PubMed  Google Scholar 

  • Faddeev, L. D. and Popov, V. N. (1967). Physics Letters B 25, 29.

    Google Scholar 

  • Feng, Y. J. and Lam, C. S. (1996). Physical Review D 53, 2115.

    CAS  Google Scholar 

  • Fock, V. A. (1937). Soviet Physics 12, 404; Schwinger, J. (1951). Physical Review 82, 664.

  • Fradkin, E. S. and Tyutin, I. V. (1970). Physical Review D 2, 2841.

    Google Scholar 

  • Garcia, J. A. and Vergara, J. D. (1996). International Journal of Modern Physics A 11, 2689.

    CAS  Google Scholar 

  • Gastmans, R., Newton, C., and Wu, T.-T. (1996). Physical Review D 54, 5302.

    CAS  Google Scholar 

  • Gastmans, R. and Wu, T.-T. (1998). Physical Review D 57, 1203.

    CAS  Google Scholar 

  • Gribov, V. N. (1978). Nuclear Physics B 139, 1.

    Google Scholar 

  • Handy, C. R. (1979). Physical Review D 19, 585.

    CAS  Google Scholar 

  • Henneaux, M. and Teitelboim, C. (1992). Quantization of Gauge Systems, Princeton University Press, Princeton, NJ.

    Google Scholar 

  • Jogleker, S. D. and Mandal, B. P. (2002). International Journal of Modern Physics A 17, 1279.

    Google Scholar 

  • Johnson, K. and Zumino, B. (1959). Physical Review Letters 3, 351.

    Google Scholar 

  • Kobe, D. H. (1985). Nuovo Cimento B 86, 155.

    Google Scholar 

  • Kummer, W. and Weiser, J. (1986). Zeitschrift für Physik C 31, 105.

    CAS  Google Scholar 

  • Lam, C. S. (1965). Nuovo Cimento 38, 1755.

    Google Scholar 

  • Landau, L. D. and Khalatnikov, I. M. (1954). Doklady Akademii Nauk SSSR 95, 773.

    CAS  Google Scholar 

  • Landau, L. D. and Khalatnikov, I. M. (1956). Zhurnal Eksperimantal’noi i Teoreticheskoi Fiziki 29, 89 [(1956). Soviet Physics-JETP 2, 69].

  • Manoukian, E. B. (1985). Nuovo Cimento A 90, 295.

    Google Scholar 

  • Manoukian, E. B. (1986). Physical Review D 34, 3739.

    CAS  Google Scholar 

  • Manoukian, E. B. (1987). Physical Review D 35, 2047.

    CAS  Google Scholar 

  • Mills, R. (1971). Physical Review D 3, 2969.

    Google Scholar 

  • Ogawa, N., Fuji, K., Miyazaki, H., Chepilko, N., and Okazaki, T. (1986). Progress of Theoretical Physics 96, 437.

    Google Scholar 

  • Oh, C. H. and Soo, C. P. (1987). Physical Review D 36, 2532.

    CAS  Google Scholar 

  • Pons, J. M., Salisbury, D. C., and Shepley, L. C. (1997). Physical Review D 55, 658.

    Google Scholar 

  • Salam, A. and Strathdee, J. (1974). Nuclear Physics B 76, 477.

    CAS  Google Scholar 

  • Sardanashvily, G. A. (1984). Annales de Physique 41, 23.

    Google Scholar 

  • Schwinger, J. (1951a). Proceedings of the National Academy of Sciences of the United States of America 37, 452.

    Google Scholar 

  • Schwinger, J. (1951b). Physical Review 82, 914.

    Google Scholar 

  • Schwinger, J. (1953a). Physical Reviews 91, 713.

    Google Scholar 

  • Schwinger, J. (1953b). Physical Reviews 91, 728.

    Google Scholar 

  • Schwinger, J. (1954). Physical Review 93, 615.

    Google Scholar 

  • Schwinger, J. (1972). Nobel Lectures in Physics 1963–1970, Elsevier, Amsterdam.

    Google Scholar 

  • Schwinger, J. (1973). In The Physicist’s Conception of Nature, J. Mehra, ed., Reidel, Dordrecht.

    Google Scholar 

  • Shifman, M. A., Vainshtein, A. I., and Zakharov, V. I. (1979). Nuclear Physics B 147, 385, 448.

    Google Scholar 

  • Slavnov, A. A. (1972). Theoretical and Mathematical Physics 10, 99.

    Google Scholar 

  • Su, J.-C. (2001). Journal of Physics G 27, 1493.

    CAS  Google Scholar 

  • Sugano, R. and Kimura, T. (1990). Physical Review D 41, 1247.

    CAS  Google Scholar 

  • Symanzik, K. (1954). Zeitschrift für Naturforschung 9, 809.

    Google Scholar 

  • Taylor, J. C. (1971). Nuclear Physics B 33, 436.

    Google Scholar 

  • Utiyama, R. and Sakamoto, J. (1977). Progress of Theoretical Physics 57, 668.

    Google Scholar 

  • Wess, J. and Zumino, B. (1974). Nuclear Physics B 70, 39.

    Google Scholar 

  • Zumino, B. (1960). Journal of Mathematical Physics 1, 1.

    Google Scholar 

  • Zwanziger, D. (1981). Nuclear Physics B 192, 259.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand

    E. B. Manoukian & S. Siranan

Authors
  1. E. B. Manoukian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Siranan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. B. Manoukian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Manoukian, E.B., Siranan, S. Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories. Int J Theor Phys 44, 53–62 (2005). https://doi.org/10.1007/s10773-005-1436-z

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-005-1436-z

KEY WORDS

Search

Navigation