Induced energy-momentum tensor of Dirac field in 2D de Sitter QED

TL;DR

This paper calculates the energy-momentum tensor of a Dirac field in 2D de Sitter space with an electric field, revealing how it depends on the electric field and mass, and discusses backreaction effects.

Contribution

It provides a detailed computation of the induced energy-momentum tensor in 2D de Sitter QED using adiabatic regularization, including trace anomaly and backreaction analysis.

Findings

Off-diagonal tensor components vanish.

Diagonal components increase with electric field, decrease with mass.

Trace anomaly matches previous results.

Abstract

We compute the expectation value of the energy-momentum tensor in the in-vacuum state of the quantized Dirac field coupled to a uniform electric field background on the Poincar$\rm\acute{e}$ path of the two dimensional de~Sitter spacetime ($\mathrm{dS}_{2}$). The adiabatic regularization scheme is applied to remove the ultraviolet divergencies from the expressions. We find, the off-diagonal components of the induced energy-momentum tensor vanishes and the absolute values of the diagonal components are increasing functions of the electric field which decrease as the Dirac field mass increases. We derive the trace anomaly of the induced energy-momentum tensor, which agrees precisely with the trace anomaly derived earlier in the literature. We have discusses the backreaction of the induced energy-momentum tensor on the gravitational field.