CANONICAL QUANTIZATION OF THE GENERALIZED AXIAL GAUGE

The incompatibility of the constraint A3 = 0 with canonical commutation rules is discussed. A canonical formulation is given of QED and QCD in the axial gauge with n1 = n2 = 0, n3 = alpha and n0 = beta, where alpha and beta are arbitrary real numbers. A Hilbert space is established for the perturbative theory, and a propagator is derived by obtaining an expression for the interaction picture gauge fields, and evaluating the vacuum expectation value of its time-ordered products in the perturbative vacuum. The propagator is expressed in terms of the parameter gamma = alpha/beta and is shown to reproduce the light cone gauge propagator when gamma = 1, and the temporal gauge propagator when gamma = 0, accommodating various prescriptions for the spurious propagator pole, including the Mandelstam-Leibbrandt and principal value prescriptions. When gamma --> infinity, the generalized axial gauge propagator leads to an expression for the propagator in the A3 = 0 gauge, though in that case the order in which the integration over k0 is performed, and the limit gamma --> infinity is taken, affects the resulting expression. Another Hilbert space is established, in which the constraints that include all interactions are implemented in a time independent fashion. It is pointed out that this Hilbert space, and the Hilbert space of the perturbative theory are unitarily equivalent in QED, but that they cannot be unitarily equivalent in QCD. Implications of this fact for the nonperturbative states of QCD are discussed.