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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2509.25488 |
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| _version_ | 1866918272703660032 |
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| author | Altschul, Brett |
| author_facet | Altschul, Brett |
| contents | In conventional relativistic quantum field theory, the discrete operators $\textbf{C}$, $\textbf{P}$, and $\textbf{T}$ are matrix operators with no renormalization scale dependence. However, in a Lorentz-violating theory with a fermion $f^μ$ term in the action, these operators may acquire nontrivial renormalization group behavior. Because the $f^μ$ term may actually be exchanged in the action for an equivalent $c^{νμ}$ 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 $\textbf{C}$, $\textbf{P}$, and $\textbf{T}-$may nonetheless be more convenient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization Group Running of the Parity Operator in Lorentz-Violating Quantum Field Theory Altschul, Brett High Energy Physics - Theory In conventional relativistic quantum field theory, the discrete operators $\textbf{C}$, $\textbf{P}$, and $\textbf{T}$ are matrix operators with no renormalization scale dependence. However, in a Lorentz-violating theory with a fermion $f^μ$ term in the action, these operators may acquire nontrivial renormalization group behavior. Because the $f^μ$ term may actually be exchanged in the action for an equivalent $c^{νμ}$ 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 $\textbf{C}$, $\textbf{P}$, and $\textbf{T}-$may nonetheless be more convenient. |
| title | Renormalization Group Running of the Parity Operator in Lorentz-Violating Quantum Field Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.25488 |