On the Zero Mode Problem of the Light-Cone Quantization

Abstract

The light-cone quantization for theories involving arbitrarily interacting scalars is studied systematically. The zero mode, which plays a special role in the light-cone quantization, is treated explicitly. Our arguments utilize a lattice regularization and the constrained path-integral method. We show, to all orders in coupling constants or the loop expansion, that the ghost fields, introduced to enforce the constraints, decouple from all the virtual processes in the infinite-volume limit. The only possibility for the light-cone quantization to deviate from the equal-time quantization is when the interaction is such that the bosonic ghost fields develop expectation values and consequently alter the location of the minimum point of the effective potential.