Bound state equations in Riemannian geometry

TL;DR

This paper develops a framework for formulating bound state equations, specifically Bethe-Salpeter equations, on arbitrary Riemannian manifolds, creating a hierarchy of equations for multipartite wave functions influenced by geometric and combinatorial factors.

Contribution

It introduces a novel geometric approach to bound state equations on Riemannian manifolds, extending traditional formulations to arbitrary geometries.

Findings

Established a hierarchy of multipartite wave function equations

Demonstrated dependence on combinatorial and metric choices

Provided a foundation for future geometric quantum field theory studies

Abstract

We study formulations of bound state (Bethe-Salpeter) equations on arbitrary Riemannian manifolds. We obtain a hierarchy of equations for multipartice wave functions. These equations, at each number of particles, depend on certain choices of combinatorial origin, which together with the metric, define the equations completely.