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.
Highlights
The theory of renormalization of the quantum electrodynamics (QED) in Minkowski spacetime is well established
Since the energy-momentum tensor is of second adiabatic order in two dimensions, we have constructed the set of the appropriate counterterms up to the second order of the adiabatic expansions; see Eqs. (45), (52), and (53)
We have shown that the off-diagonal components of the induced energy-momentum tensor vanish
Summary
The theory of renormalization of the quantum electrodynamics (QED) in Minkowski spacetime is well established. The authors of [79] considered a uniform magnetic field with conserved flux parallel to a constant energy density electric field in the dS4 and found that the density of states are proportional to the magnetic field, the scalar Schwinger effect is enhanced in the sufficiently large magnetic field They showed that in the sufficiently weak magnetic field the infrared hyperconductivity phenomenon occurs in the induced current of the scalar field. The adiabatic regularized in-vacuum state expectation value of the trace of the induced energymomentum tensor for a charged scalar field coupled to a uniform electric field background in three [102] and four [103] dimensional dS has been studied.
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