BOSONIC ZERO MODES AND GAUGE-THEORY IN DISCRETE LIGHT-CONE QUANTIZATION

We study the structure of bosonic zero modes in 3 + 1 dimensional gauge theory with a view to Hamiltonian quantization on a light-front surface - so-called discrete light-cone quantization. It suffices to consider the Maxwell field coupled to an external source to see problems, some of which we resolve here. We only 'compactify' the light-cone space x- direction. Entangled within the zero mode question is, in place of the light-cone gauge, the choice of guage conditions that enable a reduction of the formalism to a description of the independent degrees of freedom: the zero and normal modes of the fields A(perpendicular-to)i (i = 1, 2) and the zero mode of A+. In particular, a constraint equation for the zero mode of A(perpendicular-to)i is found, analogous to that in the light-cone phi4 theory. We derive the fundamental Dirac brackets and Hamiltonian for the classical reduced theory using the Dirac-Bergmann procedure.