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

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 $\mathbf{\text{CPT}}$. 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 $\mathbf{\text{C}}$, $\mathbf{\text{P}}$, and $\mathbf{\text{T}}$ operators in the $f$ theory, so that they correspond to the correct interchanges of physical particle states.