The renormalized locally covariant Dirac field

TL;DR

This paper develops a framework for the locally covariant Dirac field that includes gauge interactions, constructs renormalized quantities, and analyzes their properties and renormalization group flow.

Contribution

It introduces a new adaptation of the locally covariant Dirac field to include gauge and Yukawa backgrounds, with a method to renormalize Wick powers and analyze their scaling behavior.

Findings

Wick powers can be defined with conserved current and stress-energy tensor.

Ambiguities in renormalization are characterized.

A background field method for one-loop renormalization group flow is sketched.

Abstract

The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered products. It is shown that the Wick powers may be defined such that the current and the stress-energy tensor are conserved, and the remaining ambiguity is characterized. We sketch a variant of the background field method that can be used to determine the renormalization group flow at the one loop level from the nontrivial scaling of Wick powers.