Abstract
Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the theta-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator's light-cone poles. The obtained sub-gauge condition for the PV case is further verified by a sample calculation of the classical Yang-Mills field of two collinear ultrarelativistic point color charges. Our method does not allow one to construct a sub-gauge condition corresponding to the well-known Mandelstam-Leibbrandt prescription for regulating the gluon propagator poles.
Highlights
The obtained sub-gauge condition for the principal value (PV) case is further verified by a sample calculation of the classical Yang-Mills field of two collinear ultrarelativistic point color charges
We would like to stress that the regularizations of the gluon propagator poles given in eqs. (1.7), (1.8), (1.9) and (1.10) are by no means exhaustive, and other regularizations exist which will not be considered in this work
Motivated by the A0 = 0 gauge we propose the sub-gauge condition in eq (2.1), impose this sub-gauge condition within the functional integral, and derive an expression for the gluon propagator by carefully evaluating surface terms inside the functional integral
Summary
We will determine the sub-gauge condition that reproduces Principal Value (PV) prescription (1.9) for the k+ pole in light-cone propagator. To this end, we will adopt the same procedure we used to arrive at propagators (2.28) and (2.29) with sub-gauge conditions ∂⊥·A⊥(x− = +∞) = 0 and ∂⊥·A⊥(x− = −∞) = 0 respectively, but in reverse order. While still satisfying eq (3.5) does not allow one to construct the classical field of the color charges at the non-Abelian level It is eq (3.6) which appears to be the correct sub-gauge condition in the PV case
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