Adiabatic regularization for spin $1/2$ fields and the renormalized stress-energy tensor

TL;DR

This paper reviews adiabatic renormalization for spin-1/2 fields in expanding universes, providing explicit formulas and comparing it with DeWitt-Schwinger scheme, with applications to cosmology.

Contribution

It introduces explicit expressions for the renormalized stress-energy tensor and compares adiabatic and DeWitt-Schwinger methods for Dirac fields.

Findings

Explicit formulas for renormalized stress-energy tensor

Equivalence of adiabatic and DeWitt-Schwinger schemes

Application to cosmological scenarios

Abstract

In this article we briefly review the adiabatic renormalization program for spin 1/2 fields in expanding universes. We introduce the method and provide explicit expressions for the renormalized vacuum expectation value of the stress-energy tensor. Then, we discuss its application to some cosmological scenario of physical interest. We end up sketching out the proof that adiabatic and DeWitt-Schwinger point-splitting schemes provide the same renormalized expectation values of the stress-energy tensor for Dirac fields.