Renormalization Scheme Dependence of $\beta$-Functions In Lorentz-Violating Quantum Field Theory

TL;DR

This paper investigates how different renormalization schemes affect the $eta$-functions in Lorentz-violating quantum field theories, revealing scheme dependence in unphysical quantities but not in observable physics.

Contribution

It demonstrates that in Lorentz-violating theories, renormalization scheme choices influence $eta$-functions, highlighting the importance of scheme selection in theoretical calculations.

Findings

Renormalization scheme dependence appears in $eta$-functions.

Physically observable quantities are scheme-independent.

Scheme dependence arises due to redundancies in the Lagrangian.

Abstract

Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa theory show that when this kind of redundancy exists, different renormalization schemes may lead to different expressions for the renormalization group $\beta$-functions, even at only one-loop order. However, the renormalization group scaling of physically observable quantities appears not to share this kind of scheme dependence.