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Prog. Theor. Phys. Vol. 58 No. 3 (1977) pp. 943-958

Local Gauge Invariance of Non-Abelian Gauge Field Theory

Takao Okabayashi and Norio Nakagawa

Department of Physics, University of Tokyo, Tokyo 113

(Received February 12, 1977)

Abstract:

The non-abelian guage field theory is formulated under a gauge fixing condition of non-differential form. The condition is characterized by two properties: (i) Time-like components of gauge fields are completely determined by the other components and source fields, as in the radiation gauge. (ii) Gauge functions are timely constant arbitrary functions, and then independent of field operators. The theory is proved to be “form-invariant” under local gauge transformations. Our formulation can be regared as a legitimate formulation of an expedience in the radiation gauge formulation, where the field operator dependence of gauge functions is completely disregarded. Property (ii) makes our formulation deviate from the radiation gauge formulation to a large extent.

URL : http://ptp.ipap.jp/link?PTP/58/943/
DOI : 10.1143/PTP.58.943

[ Full Text PDF : FREE ACCESS (1354K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. C. N. Yang and R. Mills, Phys. Rev. 96 (1954), 191[APS].
2. R. Utiyama, Phys. Rev. 101 (1956), 1597[APS].
   J. Schwinger, Ann. of Phys. 2 (1957), 407[CrossRef].
   S. Glashow and M. Gell-Mann, Ann. of Phys. 15 (1961), 437[CrossRef].
3. G. 't Hooft, Nucl. Phys. B 33 (1971), 173[CrossRef]; ibid. 35 (1971), 167[CrossRef].
4. D. Gross and F. Wilczeck, Phys. Rev. Lett. 30 (1973), 1343[APS].
   H. D. Politzer, Phys. Rev. Lett. 30 (1973), 1346[APS].
   S. Coleman and D. Gross, Phys. Rev. Lett. 31 (1973), 851[APS].
5. S. Weinberg, Phys. Rev. Lett. 19 (1967), 1264[APS].
6. B. Zumino, Nuovo Cim. A 17 (1960), 547.
7. J. Schwinger, Phys. Rev. 130 (1963), 402[APS].
8. L. D. Faddeev, Teor. Mat. Fiz. 1 (1969), 1.
   V. N. Popov and L. D. Faddeev, “Perturbation Theory for Gauge-Invariant Fields”, ITF-67-36, AN UkrSSR, Kiev (1967).
9. R. L. Arnowitt and S. I. Fickler, Phys. Rev. 127 (1962), 1821[APS].
   T. Goto and R. Utiyama, Prog. Theor. Phys. Suppl. Nos. 37 & 38 (1966), 322[PTP].
10. T. Okabayashi, Prog. Theor. Phys. 48 (1972), 1375[PTP].
11. T. Okabayashi and Y. Yoshihuku, Prog. Theor. Phys. 54 (1975), 878[PTP].
12. J. Schwinger, Phys. Rev. 127 (1962), 324[APS].
13. W. Konetschny and W. Kummer, Nucl. Phys. B 100 (1975), 106[CrossRef]; ibid. 108 (1976), 397[CrossRef].
    W. Kummer, Acta Phys. Austr. Suppl. 15 (1976), 423.
    C. Callan, R. Dashen and D. Gross, Phys. Lett. B 63 (1976), 334[CrossRef].
14. Y. P. Yao, J. Math. Phys. 5 (1964), 1319[CrossRef].
15. T. Okabayashi and H. Kikugawa, Prog. Theor. Phys. 52 (1974), 1687[PTP]; ibid. 52 (1974), 1953[PTP].
16. T. Okabayashi, Prog. Theor. Phys. 46 (1971), 634[PTP].
17. T. Okabayashi, Prog. Theor. Phys. 50 (1973), 661[PTP]; ibid. 50 (1973), 1046[PTP].
    T. Okabayashi and H. Kikugawa, Prog. Theor. Phys. 51 (1974), 1239[PTP].
18. T. Okabayashi, Forts. Phys. 24 (1976), 619.
19. D. G. Boulware, Ann. of Phys. 56 (1970), 140[CrossRef].
20. T. Okabayashi, Prog. Theor. Phys. 51 (1974), 592[PTP].
21. J. Schwinger, Phys. Rev. 125 (1962), 1043[APS].
22. T. Okabayashi, T. Sasaki and K. Yoshikawa, Prog. Theor. Phys. 47 (1972), 293[PTP].
23. T. Okabayashi, Prog. Theor. Phys. 47 (1972), 1714[PTP].
24. J. Schwinger, Nuovo Cim. 30 (1963), 278.
25. T. Okagayashi and N. Nakagawa, “Time-Like Axial Gauge Formalism”, Tokyo University preprint UT-274 (1976), unpublished.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 61 No. 5 (1979) pp. 1499-1514 :

   Quanta of Non-Abelian Gauge Field Can Be Transversal?

   Takao Okabayashi

2. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 201-213 :

   T^*-Product Convention for Quasi-Linear Systems and for Transverse Non-Abelian Gauge Fields

   Takao Okabayashi

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