Adiabatic expansions for Dirac fields, renormalization, and anomalies

TL;DR

This paper presents a new iterative method for determining the adiabatic expansion of Dirac field modes in external backgrounds, improving regularization and renormalization techniques, and analyzing anomalies in various spacetime models.

Contribution

The authors introduce a novel iterative approach to resolve ambiguities in adiabatic expansions of Dirac fields, enhancing the regularization scheme and analyzing anomalies in different backgrounds.

Findings

Consistent adiabatic expansion for Dirac modes in external fields

Reproduction of known axial and conformal anomalies

Application to four-dimensional FLRW spacetime with Yukawa coupling

Abstract

We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to improve the adiabatic regularization/renormalization scheme. We provide details on the application of the method for Dirac fields living in a four-dimensional Friedmann-Lemaitre-Robertson-Walker spacetime with a Yukawa coupling to an external scalar field. We check the consistency of our proposal by working out the conformal anomaly. We also analyze a two-dimensional Dirac field in Minkowski space coupled to a homogeneous electric field and reproduce the known results on the axial anomaly. The adiabatic expansion of the modes given here can be used to properly characterize the allowed physical states of the Dirac fields in the above external backgrounds.