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

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 Poincaré patch of the two-dimensional de Sitter spacetime (dS₂). The adiabatic regularization scheme is applied to remove the ultraviolet divergencies from the expressions. Then we obtain a finite result for the induced energy-momentum tensor that varies continuously under a continuous change of the electric field strength and the Dirac field mass. We find that the off-diagonal components of the induced energy-momentum tensor vanish. The absolute values of the diagonal components increase as the electric field increases and decrease as the Dirac field mass increases except in the very near vicinity of their zero points. 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 discussed the backreaction of the induced energy-momentum tensor on the gravitational field of the dS₂.