On the Stress-Energy Tensor of Quantum Fields in Curved Spacetimes -   Comparison of Different Regularization Schemes and Symmetry of the   Hadamard/Seeley-DeWitt Coefficients
  We review a few rigorous and partly unpublished results on the regularisation of the stress-energy in quantum field theory on curved spacetimes: 1) the symmetry of the Hadamard/Seeley-DeWitt coefficients in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. 
Thomas-Paul Hack and Valter Moretti
gr-qc hep-th math-ph math.MP