Exact Results in Quantum Theory

The Klein-Gordon equation has several interesting and relevant propagators (also called Green’s functions or two-point functions): the forward/backward propagator, the Pauli-Jordan propagator, the Feynman propagator, the Wightman two-point function. In this talk I will discuss an approach to construct propagators on curved spacetimes. This approach can also be applied for non-smooth metrics and when external electromagnetic fields are present. For static spacetimes, I will show that the Feynman propagator can be constructed as the limit of the resolvent of the Klein-Gordon operator. I will then argue that this construction can be generalized to some non-static spacetimes.