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 $ \omega $ 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 $ \omega ^{-{\epsilon\over2}} \epsilon^{-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 $ \omega $. However, for the self energy on the spacelike Wilson line we obtain an unexpected double pole at $ \epsilon=0 $, using dimensional regularization in $ 4-\epsilon $ dimensions.