The Leibbrandt–Mandelstam prescription for general axial gauge one-loop integrals

Abstract

It is well known that, in doing light-cone gauge calculations, it is mandatory to regularize the unphysical (q n)−β poles by use of the Leibbrandt–Mandelstam prescription. This technique is also applied to general axial gauges and it is proved that it is a suitable regularization procedure for these gauges as well. In order to find the relation between the Leibbrandt prescription and the more familiar principal value prescription with its simpler Lorentz structure the temporal gauge limit n→0 is performed (within dimensional regularization). Although this limit is found to be singular for multiple poles, the analytically regularized one-loop integrals agree with the results obtained within the principal value technique for the temporal gauge.

Probing negative-dimensional integration: two-loop covariant vertex and one-loop light-cone integrals

“…Leibbrandt prescription [16] in this context. In parallel, it became clear that all those pathologies do arise because the PV prescription violates causality and once causality is carefully taken into account, no prescription is in fact needed [17].…”

“…Soon after it has been shown that both prescriptions were in fact equivalent and became known as the ML prescription. Still later on the prescription has been generalized to deal with generic noncovariant axial gauges and sometimes it has been referred as the generalized Mandelstam-Leibbrandt prescription [16] in this context. In parallel, it became clear that all those pathologies do arise because the PV prescription violates causality and once causality is carefully taken into account, no prescription is in fact needed [17].…”