Covariant and dynamical reduction for principal bundle field theories

Reduction for field theories with symmetry can be done either covariantly-that is, on spacetime-or dynamically-that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a "sea of rigid bodies" with and appropriate interbody coupling potential.