QCD in the axial gauge representation

Within the canonical Weyl gauge formulation, the axial gauge representation of QCD on a torus is derived. The resolution of the Gauss law constraint is achieved by applying unitary gauge fixing transformations. The result of this formal development is a Hamiltonian explicitly formulated in terms of unconstrained degrees of freedom. Novel features of this Hamiltonian are the non-perturbative dynamics of two-dimensional degrees of freedom appearing in the gauge-fixing procedure, such as Jacobian and centrifugal barrier. These two-dimensional fields appear to be essential for the infrared properties of the theory. The global residual gauge symmetries of QCD are established in this representation. It is shown that SU(N) gauge theories may exhibit at most N-1 massless vector (gauge) bosons. The implications for the phase structure of non-abelian gauge theories (QCD, Georgi-Glashow model) are discussed. 42 refs., 1 fig