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

We study the structure of bosonic zero modes in 3 + 1 dimensional gaug e theory with a view to Hamiltonian quantization on a light-front surf ace - so-called discrete light-cone quantization. It suffices to consi der the Maxwell field coupled to an external source to see problems, s ome of which we resolve here. We only 'compactify' the light-cone spac e x- direction. Entangled within the zero mode question is, in place o f the light-cone gauge, the choice of guage conditions that enable a r eduction 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 equ ation 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 b rackets and Hamiltonian for the classical reduced theory using the Dir ac-Bergmann procedure.