Abstract
In this paper we study the axial anomaly in Very Special Relativity Electrodynamics using Pauli-Villars and dimensional regularization of ultraviolet divergences and Mandelstam-Leibbrandt regularization of infrared divergences. We compute the anomaly in 2 and 4 dimensional space-time. We find that this procedure preserves the vector Ward identity(charge conservation) and reproduce the standard axial anomaly in 2 and 4 dimensions without corrections from VSR. Finally, we show how to obtain the anomaly in the path integral approach.
Highlights
The Standard Model of particle physics (SM) is a very successful theory
In this paper we study the axial anomaly in two and four dimensions using Pauli-Villars (PV) and dimensional(DR) regularization of ultraviolet divergences and ML prescription for infrared divergences
We show explicitly that the vector current is conserved and that the axial anomaly is the same we get in Lorentz invariant electrodynamics, without any correction from VSR
Summary
The Standard Model of particle physics (SM) is a very successful theory. With the discovery of the Higgs boson at CERN, its particle composition was completed [1]. The most interesting of these subgoups are Sim(2) and Hom(2) Using these subgroups new terms are allowed such that the neutrino get a mass [5]. The authors of [22] tried to compute the axial anomaly in four dimensions using the prescription to treat γ5 introduced in [23]. In this paper we study the axial anomaly in two and four dimensions using Pauli-Villars (PV) and dimensional(DR) regularization of ultraviolet divergences and ML prescription for infrared divergences. Our result relies on two properties of the ML prescription: First, it allows shifting of the loop momentum variable (which implies gauge invariance) and second, it respects naive power counting According to this result, the VSRSM must be free from anomalies and consistent.
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