Quantum Field Theories in the Infinite-Momentum Frame. I. Quantization of Scalar and Dirac Fields

Abstract

Renormalizable coupled scalar and Dirac field theories are quantized in equal-${x}^{+}$ surfaces (called light fronts). Schwinger's action principle is employed to deduce the correct canonical equal-${x}^{+}$ (anti-) commutation relations. These theories are shown to be Lorentz-invariant. Generalized Schwinger conditions for a quantum field theory to be Lorentz-invariant are given and discussed in an appendix. Spectral sum rules are derived. Leading singularities of Green's functions and products of field operators near the light cone are studied and the implications to current algebra sum rules are discussed. We also discuss some of the delicate features of the light-front formulation.