We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations. © 2008 Elsevier B.V. All rights reserved.
Manno, G., Pohjanpelto, J., Vitolo, R. (2008). Gauge invariance, charge conservation, and variational principles. JOURNAL OF GEOMETRY AND PHYSICS, 58(8), 996-1006 [10.1016/j.geomphys.2008.03.006].
Gauge invariance, charge conservation, and variational principles
MANNO, GIOVANNI;
2008
Abstract
We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations. © 2008 Elsevier B.V. All rights reserved.
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