# On the Stress-Energy Tensor of Quantum Fields in Curved Spacetimes - Comparison of Different Regularization Schemes and Symmetry of the Hadamard/Seeley-DeWitt Coefficients

February 23, 2012

We review a few rigorous and partly unpublished results on the regularisation
of the stress-energy in quantum field theory on curved spacetimes: 1) the
symmetry of the Hadamard/Seeley-DeWitt coefficients in smooth Riemannian and
Lorentzian spacetimes 2) the equivalence of the local $\zeta$-function and the
Hadamard-point-splitting procedure in smooth static spacetimes 3) the
equivalence of the DeWitt-Schwinger- and the Hadamard-point-splitting procedure
in smooth Riemannian and Lorentzian spacetimes.

Keywords:

Hadamard states, DeWitt-Schwinger- and the Hadamard-point-splitting procedure