Canonical quantization of gauge theories

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Abstract
A canonical quantization scheme in a Hilbert space with positive-definite metric is proposed for local gauge theories, based on Dirac's general theory of singular dynamical systems. A theorem on the subsidiary conditions, permitting a perturbation treatment, is stated and proved. Unitarity in the subspace of allowed states is demonstrated. The method is applied to the case of free electrodynamics in a nonlinear gauge and Yang-Mills theory in the convariant Feynman gauge. The description does not require introduction of ghost particles. The rules for calculating graphs are shown to be equivalent to those in a Lagrangian approach with a ghost.