  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.
