Perturbative Calculations with the First Order Form of Gauge Theories

TL;DR

This paper explores the quantization of the first order form of gauge theories, like Yang-Mills and Einstein-Hilbert, using Faddeev-Popov, highlighting simplified interaction vertices and analyzing one-loop thermal energy-momentum corrections.

Contribution

It derives Feynman rules for first order gauge theories and examines their one-loop thermal energy-momentum tensor corrections, offering a new perspective on quantization simplicity.

Findings

Interaction vertices are momentum-independent.

Derived Feynman rules for first order gauge theories.

Computed one-loop thermal energy-momentum tensor corrections.

Abstract

The first and second order form of gauge theories are classically equivalent; we consider the consequence of quantizing the first order form using the Faddeev-Popov approach. Both the Yang-Mills and the Einstein-Hilbert actions are considered. An advantage of this approach is that the interaction vertices are quite simple, being independent of momenta. It is necessary however to consider the propagator for two fields (including a mixed propagator). We derive the Feynman rules for both models and consider the one loop correction for the thermal energy momentum tensor.