Creation of spin $1/2$ particles and renormalization in FLRW spacetime

TL;DR

This paper develops a formalism using adiabatic regularization and WKB ansatz to compute the number density and energy-momentum of spin 1/2 particles in flat FLRW spacetimes, aligning with known anomalies.

Contribution

It extends adiabatic regularization techniques from scalar fields to fermions in curved spacetime, providing a simplified approach for spin 1/2 particles.

Findings

Conformal and axial anomalies match existing results.

Formalism accurately computes particle densities and energy-momentum in FLRW.

Method is consistent with other renormalization techniques.

Abstract

Within the framework of adiabatic regularization, we present a simple formalism to calculate number density and renormalized energy-momentum density of spin 1/2 particles in spatially flat FLRW spacetimes using an appropriate WKB ansatz for the adiabatic expansion for the field modes. The conformal and axial anomalies thus found are in exact agreement with those obtained from other renormalization methods. This formalism can be considered as an appropriate extension of the techniques originally introduced for scalar fields, applicable to fermions in curved space.