Physics – Mathematical Physics
Scientific paper
2007-12-12
J.Phys.A41:344002,2008
Physics
Mathematical Physics
13 pages, 1 figure
Scientific paper
10.1088/1751-8113/41/34/344002
We give an exposition of the parametrization method of Kuchar [1973] in the context of the multisymplectic approach to field theory, as presented in Gotay and Marsden [2008a]. The purpose of the formalism developed herein is to make any classical field theory, containing a metric as a sole background field, generally covariant (that is, "parametrized," with the spacetime diffeomorphism group as a symmetry group) as well as fully dynamic. This is accomplished by introducing certain "covariance fields" as genuine dynamic fields. As we shall see, the multimomenta conjugate to these new fields form the Piola-Kirchhoff version of the stress-energy-momentum tensor field, and their Euler-Lagrange equations are vacuously satisfied. Thus, these fields have no additional physical content; they serve only to provide an efficient means of parametrizing the theory. Our results are illustrated with two examples, namely an electromagnetic field and a Klein-Gordon vector field, both on a background spacetime.
Gotay Mark J.
Lopez Marco Castrillon
Marsden Jerrold E.
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