Light-cone quantization: Study of a soluble model with q-number anticommutator

A massless Dirac field interacting with a massive vector meson in two-dimensional space--time is considered in an attempt to gain further understanding of interacting systems quantized in light-cone coordinates. It is shown that the solution is equivalent, not to the same system quantized on a spacelike surface, but rather to a single-component fermion model already known in the literature. The commutation relations among the field variables are found to be interaction dependent, with the fermion anticommutator having a q-number term in addition to the usual delta function. This latter feature may be traced to the fact that the number of degrees of freedom of the light-cone quantized system is fewer than that of the single-component fermion model to which it is equivalent, with this discrepancy in the number of independent dynamical variables being exactly compensated by the interaction-dependent terms in the commutation relations. Some possible applications to four-dimensional space--time are briefly discussed