  We review a few rigorous and partly unpublished results on the regularisation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.
