Chiral Poincare transformations and their anomalies

TL;DR

This paper investigates chiral extensions of Poincaré transformations in fermionic theories, revealing anomalies through Jacobian calculations, which may have implications for four-dimensional bosonization.

Contribution

It introduces and computes anomalies for chiral Poincaré transformations in fermionic systems using proper time regularization.

Findings

Chiral Poincaré transformations generate anomalies due to nontrivial Jacobians.

Anomalies are computed explicitly for massive fermions coupled to Abelian fields.

Results suggest potential relevance to four-dimensional bosonization.

Abstract

I consider global transformations of a Dirac fermion field, that are generated by the generators of Poincar'e transformations, but with a \gamma_5 appended. Such chiral translations and chiral Lorentz transformations are usually not symmetries of the Lagrangian, but naively they are symmetries of the fermionic measure. However, by using proper time regularization in Minkowski space, I find that they in general give rise to a nontrivial Jacobian. In this sense they have "anomalies". I calculate these anomalies in a theory of a massive fermion coupled to an external Abelian vector field. My motivation for considering chiral Poincar'e transformations is the possibility that they are relevant to bosonization in four dimensions.