Abstract
The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction — the axial coupling of fermions with a constant vector field bμ — is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.
Highlights
The issue intensively claimed in the literature on the generation of a CPTodd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction — the axial coupling of fermions with a constant vector field bμ — is mistaken
To all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector bμ
The proof of this fact is based on general theorems of perturbative quantum field theory, where the Lowenstein-Zimmermann subtraction scheme in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method [45] is adopted
Summary
We start by considering an action for extended QED with a term which violates the Lorentz and CPT symmetries in the matter sector only. In addition to the Slavnov-Taylor identity (2.8), the classical action Σ(s−1) (2.1) is characterized by the gauge condition, the ghost equation and the antighost equation: δΣ(s−1) δb. It has to be pointed out that, since the Lorentz breaking ΣSB (2.3) is not linear in the quantum fields, it shall be submitted to renormalization It is a soft breaking, its ultraviolet (UV) power-counting dimension is less than 4, namely 3. To the action Σ(s−1) (2.1), a term depending on βμ, such as: It can be verified the following classical Ward identity WLαβΣ(s−1) = 0 , so that, at βμ = 0, it reduces to the broken Lorentz Ward identity (2.28).
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