Exact Results in Quantum Theory

The expectation value of the energy-momentum tensor in the in-vacuum state of the Dirac field, which is quantized in the Poincaré patch of 2-dimensional de Sitter space-time in the presence of a uniform electric field background, has been computed. The ultraviolet divergences are removed by applying the adiabatic regularization method. Then, we obtain the finite and continuous expressions of the parameters electric field and Dirac field mass for the energy-momentum tensor components. We show that the off-diagonal components of the energy-momentum tensor vanish, and 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 points at which these expressions become zero. We have computed the trace anomaly of the energy-momentum tensor, which agrees precisely with the trace anomaly derived earlier in the literature. In this talk, I will discuss the back-reaction effect of the induced energy-momentum tensor on the gravitational field of the 2-dimensional de Sitter spacetime.