The Mandelstam-Leibbrandt prescription in light-cone quantized gauge theories

Abstract

Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.

Light-Cone Quantization of the Schwinger Model

“…Now we see that the field, Ψ − , is isomorphic to the left-moving component of a free, massless Fermi field and it has no dependence on the ghost field even through the spurion; both of these properties are to be expected in light-cone gauge 3) . Even with the modifications of the spurions the physics contained in the light-cone gauge solution is the same as that in the Landau gauge solution.…”

The common elements of atomic and hadronic physics

“…One can utilize the Mandelstam-Liebbrandt method [10,11,12] to regulate the singularities at k + = 0 which appear in LF time-ordered perturbative matrix elements and loop integrals when quantizing in light-cone gauge. Alternatively, one can choose to quantize a gauge theory in a covariant gauge such as Feynman gauge [13] and avoid these complications.…”