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2016

Motohashi, Hayato, Suyama, Teruaki, Takahashi, Kazufumi

Regardless of the long history of gauge theories, it is not well recognized under which condition gauge fixing at the action level is legitimate.

We address this issue from the Lagrangian point of view, and prove the following theorem on the relation between gauge fixing and Euler-Lagrange equations: In any gauge theory, if a gauge fixing is complete, i.e., the gauge functions are determined uniquely by the gauge conditions, the Euler-Lagrange equations derived from the gauge-fixed action are equivalent to those derived from the original action supplemented with the gauge conditions.
Otherwise, it is not appropriate to impose the gauge conditions before deriving Euler-Lagrange equations as it may in general lead to inconsistent results.
The criterion to check whether a gauge fixing is complete or not is further investigated.

J. Eiesland, Trans. Amer. Math. Soc. 27
1925
Earlier work this paper cites.
J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, J. Cosmol. Astropart. Phys. 1502
Original
1952
Earlier work this paper cites.
T. Regge and J. A. Wheeler, Phys. Rev. 108
1957
Earlier work this paper cites.
E. Noether, Gott. Nachr. 1918
1971
Earlier work this paper cites.
G. W. Horndeski, Int.J.Theor.Phys. 10
1974
Earlier work this paper cites.
R. S. Palais, Comm. Math. Phys. 69
1979
Earlier work this paper cites.
H. Kodama and M. Sasaki, Prog. Theor. Phys. Suppl. 78
1984
Earlier work this paper cites.
M. A. Rubin and C. R. Ordóñez, J. Math. Phys. 25
1984
Earlier work this paper cites.
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992)
1992
Earlier work this paper cites.
J. M. Pons, Int. J. Mod. Phys. A 11
1996
Earlier work this paper cites.
J. Garriga, X. Montes, M. Sasaki, and T. Tanaka, Nucl. Phys. B513
1999
Earlier work this paper cites.
H. Kodama, A. Ishibashi, and O. Seto, Phys. Rev. D 62
2000
Earlier work this paper cites.