ON ZERO MODES AND GAUGE-FIXING IN LIGHT-CONE QUANTIZED GAUGE-THEORIES

Discretized light-cone quantization potentially solves QCD in 3+1 dime nsions. However the zero Fourier modes of bosonic fields are an outsta nding formal problem. Here we study these zero modes of gauge bosons b ut only for QED in 3+1 dimensions. Crucial to the present treatment is a set of gauge conditions which differ in different Fourier sectors o f the theory. We shall specify in which of the sectors the conventiona l light-cone gauge A+=0 is justified. In the new gauge setting almost all of the zero modes are not dynamical but constrained fields. Due to antiperiodic boundary conditions on the fermionic fields there are no fermion zero modes. But fermions complicate the non-perturbative stru cture of the constraints insofar as they generate coupled linear equat ions for the boson modes. Iterative solutions are given.