Equivalence of Adiabatic and DeWitt-Schwinger renormalization schemes

TL;DR

This paper demonstrates that adiabatic regularization and DeWitt-Schwinger point-splitting methods yield identical results for the renormalized stress-energy tensor of spin-1/2 fields, extending known scalar field equivalences.

Contribution

It proves the equivalence of adiabatic and DeWitt-Schwinger renormalization schemes for spin-1/2 fields and shows their agreement at all orders in FLRW universes.

Findings

Both methods produce identical renormalized stress-energy tensors.

The DeWitt-Schwinger expansion matches the adiabatic regularization at all orders.

Adiabatic method effectively computes higher order DeWitt coefficients.

Abstract

We prove that adiabatic regularization and DeWitt-Schwinger point-splitting provide the same result for the renormalized expectation values of the stress-energy tensor for spin-$1/2$ fields. This generalizes the equivalence found for scalar fields, which is here recovered in a different way. We also argue that the coincidence limit of the DeWitt-Schwinger proper time expansion of the two-point function exactly agrees with the analogous expansion defined by the adiabatic regularization method at any order (for both scalar and spin-$1/2$ fields). We also illustrate the power of the adiabatic method to compute higher order DeWitt coefficients in FLRW universes.