The bosonic and fermionic propagators under an external electromagnetic field in a Euclidean manifold

In this paper, we will calculate the bosonic as well as fermionic propagators under classical homogeneous and constant magnetic and electric fields in a Euclidean space. For this, we will reassess the Ritus' method for calculating the Feynman propagator.

Quantum Propagators for Geodesic Congruences

Using the Raychaudhuri equation, we show that a quantum probability amplitude (Feynman propagator) can be univocally associated to any timelike or null affinely parametrized geodesic congruence.

Summing over Spacetime Dimensions in Quantum Gravity

Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand taken in the absence of quantum gravity.

The Massive Feynman Propagator on Asymptotically Minkowski Spacetimes II

We consider the massive Klein–Gordon equation on short-range asymptotically Minkowski spacetimes. Extending our results in [7], we show that the Klein–Gordon operator with Feynman-type boundary conditions at infinite times is invertible and that its inverse, called the Feynman inverse, satisfies the microlocal conditions of Feynman parametrices in the sense of Duistermaat and Hörmander. This supplements the recent work of Vasy [10] with more explicit techniques.

Feynman propagators on static spacetimes

We consider the Klein–Gordon equation on a static spacetime and minimally coupled to a static electromagnetic potential. We show that it is essentially self-adjoint on [Formula: see text]. We discuss various distinguished inverses and bisolutions of the Klein–Gordon operator, focusing on the so-called Feynman propagator. We show that the Feynman propagator can be considered the boundary value of the resolvent of the Klein–Gordon operator, in the spirit of the limiting absorption principle known from the theory of Schrödinger operators. We also show that the Feynman propagator is the limit of the inverse of the Wick rotated Klein–Gordon operator.