Quantization of a gauge theory with independent metric and connection fields

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Abstract
We carry out the Hamiltonian quantization of a member of a class of gauge theories in which the internal metric becomes an independent degree of freedom and the gauge group is generalized to SL(N,C). The Hamiltonian quantization is carried out both in a gauge where only the SU(N) symmetry is manifest and in a gauge-invariant way. These theories have been proposed by Cahill, and they also arise as the nongravitational sector of a unified theory of gravitational and gauge fields which has been proposed by one of us (J.D.). The physical degrees of freedom are identified and a relativistically invariant functional generator is constructed. The resulting quantum theory is stable, but not perturbatively renormalizable.