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

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.