Aspects of the Equivalence Between the $f^{\mu}$ and $c^{\nu\mu}$ Terms in Lorentz-Violating Quantum Field Theory

TL;DR

This paper explores the quantum-level equivalence between two Lorentz-violating coefficients in quantum field theory, extending classical results and providing explicit transformations and symmetry prescriptions.

Contribution

It generalizes classical equivalence between $c$ and $f$ coefficients to the quantum level, including explicit transformations and symmetry modifications.

Findings

No additional anomalies arise at the quantum level

Explicit spinorial transformations interconvert $c$ and $f$ terms

Modified $C$, $P$, $T$ operators correspond to physical state interchanges

Abstract

It is known that in Lorentz-violating effective field theory, there is a classical equivalence between certain coefficients ($c$ and $f$), in spite of the fact that the operators the two types of coefficients describe appear to have opposite behaviors under $\textbf{CPT}$. This paper is a continuation of previous work extending this equivalence to the quantum level: generalizing the explicit spinorial point transformations that interconvert the $c$ and $f$ terms; demonstrating that the transformations do not give rise to any additional anomaly terms as the quantum level; and giving explicit prescriptions for modifying the $\textbf{C}$, $\textbf{P}$, and $\textbf{T}$ operators in the $f$ theory, so that they correspond to the correct interchanges of physical particle states.