The generating functional for the electromagnetic interaction in the strong gravitational field

TL;DR

This paper develops a generating functional approach for electromagnetic interactions in curved spacetime, enabling calculation of scattering amplitudes and Feynman rules near strong gravitational fields like black holes.

Contribution

It introduces a generalized generating functional for electromagnetic fields in curved spacetime, facilitating analysis of quantum electrodynamic processes in strong gravitational fields.

Findings

Derived generating functionals for free Dirac and electromagnetic fields.

Obtained scattering amplitudes for Compton scattering and electron-positron annihilation.

Formulated generalized Feynman rules for curved spacetime.

Abstract

This article is devoted problems of electromagnetic interaction in curved spacetime. Such problems exist, in particular, when we investigate electromagnetic quantum processes near black holes. The generalization of reduction formalism permits to find formulas for scattering matrices. For the free Dirac and electromagnetic fields corresponding generating functionals are calculated. Next we have found the generating functional for the interaction of these fields. This result holds the central position in our investigation. By means of generating functionals and reduction formulas we have obtained the scattering amplitudes for elementary electrodynamic processes: Compton scattering and the annihilation of electron-positron pair (for the tree-level approximation). On the base of these results we have formulated the generalized Feynman rules for the electromagnetic interaction in curved spacetime. Another electrodynamic processes can be studied by means of these Feynman rules and crossing-symmetry. The generating functional can be used to study problems of quantum statistics in curved spacetime.