Quantum field theory on a curved background

In this report my purpose is to study an useful mathematical instrument: the tensor and spinor Green functions or propagators associated to a given curved space-time. These propagators are extentiona of the scalar propagator $D$ of Jordan–Pauli which plays an important role in the old quantum field theory. A formal introduction has been given, some years ago, bу В. and С. DeWitt (see also Mensky).