Bosonic zero modes and gauge theory in discrete light-cone quantization

Abstract

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 spacex− 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 fieldsA⊥i (i=1,2) and the zero mode ofA+. In particular, a constraint equation for the zero mode ofA⊥i is found, analogous to that in the light-cone ϕ4 theory. We derive the fundamental Dirac brackets and Hamiltonian for the classical reduced theory using the Dirac-Bergmann procedure.