Gauge theories in the light-cone gauge

Abstract

A canonical formulation, using equal-time commutation rules for canonically conjugate operator-valued fields, is given for quantum electrodynamics and Yang-Mills theory in the light-cone gauge. A gauge-fixing term is used that avoids all operator constraints by providing a canonically conjugate momentum for every field component. The theory is embedded in a space in which the light-cone gauge condition and all of Maxwell's equations hold. Interaction picture fields and the photon and gluon propagators in the light-cone gauge are evaluated for two alternate representations of the longitudinal and timelike components of gauge fields. One representation makes use of the entire momentum space to represent these gauge field components as superpositions of ghost annihilation and creation operators. The other uses only ghost excitations with {ital k}{sub 3}{gt}0 for the longitudinal modes of {ital A}{sub {ital i}}, but restricts the gauge-fixing field to ghost excitations with {ital k}{sub 3}{lt}0. It is shown that the former mode leads to a formulation that corresponds to the principal-value (PV) prescription for the extra pole in this gauge, the latter to the Mandelstam-Leibbrandt (ML) prescription. Nevertheless the underlying theory for these two cases is identical. In particular, for QED both modes give identical time evolution, within a physicalmore » subspace in which constraints are implemented, as does QED in the Coulomb gauge. It is therefore concluded that canonical formulations of the light-cone gauge cannot be a basis for preferring the ML to the PV prescription for the extra pole at {ital k}{sub 0}={ital k}{sub 3} in the light-cone propagator.« less