Canonical quantization of non-Abelian gauge theories in the axial gauge

Abstract

We explore canonical quantization in the axial gauge, with special reference to the problems of (i) additional gauge fixing; and (ii) the infrared infinities which occur in eliminating the dependent variables. We show that the freedom inherent in (i) permits the removal of (ii), resulting in a Hamiltonian with no explicit infinities, generating the proper equations of motion. This does not mean, however, that all matrix elements of the Hamiltonian will be finite. In particular, the bare-vacuum-expectation value of $H$ still contains an infrared divergence.