Dynamical Constraints in the Nonsymmetric Gravitational Theory

The antisymmetric sector of the nonsymmetric gravitational theory (NGT) does not possess a rigorous gauge invariance which allows redundant degrees of freedom in $g_{[\mu\nu]}$ to be removed by gauge fixing conditions. Since there are in general six dynamical degrees of freedom in $g_{[\mu\nu]}$, we impose, by means of Lagrange multiplier fields in the action, a set of covariant constraints on the $g_{[\mu\nu]}$. The canonical Hamiltonian constraints in the weak field approximation for the antisymmetric sector yield a Hamiltonian energy bounded from below. An analysis of the Cauchy evolution in terms of an expansion of the antisymmetric sector about a symmetric Einstein background, shows that arbitrarily small antisymmetric Cauchy data can lead to smooth evolution.