Nonsymmetric Gravitational Theories in Hamiltonian Form

Abstract

The dynamics of a class of nonsymmetric gravitational theories are presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the densitized components of the inverse of the fundamental tensor as conjugate momenta. The phase space of the symmetric sector is enlarged over that of conventional treatments of general relativity by a canonical pair that represents the metric density and its conjugate, removable by imposing strongly an associated pair of second-class constraints and introducing Dirac brackets. In the antisymmetric sector, all six components of the fundamental tensor contribute conjugate pairs for the massive theory, and the absence of additional constraints gives six configuration space degrees of freedom per space–time point.