Pole-Free Gluon Propagators In Extended Temporal Gauge

Abstract

A central principle in the formulation of Yang-Mills theories is the invariance of the Lagrangian under local gauge transformations. However, this gauge symmetry introduces significant challenges in the quantization of gauge fields, primarily due to the inclusion of non-physical degrees of freedom in the path integral formalism. The Faddeev-Popov method is widely used to address these challenges by imposing a gauge condition, which eliminates these non-physical modes. This work focuses on the quantization of Yang-Mills fields in noncovariant gauges, specifically the temporal gauge. Noncovariant gauges are advantageous in that they decouple ghost fields during loop calculations. Nevertheless, they come with their own set of complications, notably the appearance of singularities or poles in gluon Green functions, particularly of the form  The treatment of these poles is not straightforward and has been a topic of various proposed methods in the literature. In this study, we adopt the technique developed by Veliev, Karnaukhov, and Fainberg, which extends the gauge condition to effectively remove these poles, resulting in a regularized, pole-free gluon propagator. Our investigation explores an extended version of the temporal gauge which smoothly transitions into the standard temporal gauge. Through this extension and after completing the standard quantization process, we derive Green functions that are free of singularities.