New Features of the Mandelstam-Leibbrandt Lightcone Gauge

Abstract

This is about new unexpected features of the Mandestam-Leibbrandt prescription found as applied to spacelike Wilson lines. The regularization parameter $ ω$ in the M-L denominator for the spurious poles has to be kept throughout the calculation till the very end or else the integrals do not make sense. We get various `ambiguous' terms of the form $ ω^{-{ε\over2}} ε^{-2} $ which are not controlled by any sort of Ward identity. These terms cancel out in the sum and the final result is independent of $ ω$. However, for the self energy on the spacelike Wilson line we obtain an unexpected double pole at $ ε=0 $, using dimensional regularization in $ 4-ε$ dimensions.