In conventional relativistic quantum field theory, the discrete operators $C$, $P$, and $T$ are matrix operators with no renormalization scale dependence. However, in a Lorentz-violating theory with a fermion $f^{\mu }$ term in the action, these operators may acquire nontrivial renormalization group behavior. Because the $f^{\mu }$ term may actually be exchanged in the action for an equivalent $c^{\nu \mu }$ term, the scale dependence depends explicitly on the renormalization scheme, even at one-loop order. The scheme dependence means it is always possible to set the scale dependence parameter $1-X$ to zero, but for analyses of some high-energy electron-photon processes, using a scheme with $X=0$—and thus definite scale dependences for $C$, $P$, and $T$—may nonetheless be more convenient.

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• Hypothetical particle physics models
• Renormalization group
• CPT symmetry
• Lorentz symmetry