Investigation of the High Energy Behaviours of the Scalar Particle Scattering Amplitude in the Gravitational Field by Functional Approach

TL;DR

This paper derives closed-form expressions for scalar particle scattering amplitudes in gravitational fields using functional integrals, revealing faster cross section growth compared to electromagnetic cases and identifying discrete energy levels in Newtonian potential.

Contribution

It introduces a functional integral approach to compute scattering amplitudes in gravitational fields, providing new insights into energy dependence and particle energy levels.

Findings

Cross section increases more rapidly with energy in gravitational scattering.

Closed-form expressions for Green functions and amplitudes are obtained.

Discrete energy levels are identified in the Newton potential.

Abstract

Closed expressions for the Green function and amplitude of the scalar particle scattering in the external gravitational field $g_{\mu\nu}(x)$ are found in the form of functional integrals. It is shown that, as compared with the scattering on the vector potential, the tensor character of the gravitational field leads to a more rapid increase of the cross section with increasing energy. Discrete energy levels of particles are obtained in the Newton potential.