Multi-channel Bethe-Salpeter equation

TL;DR

This paper introduces a comprehensive multi-channel Bethe-Salpeter equation framework that simultaneously solves for all relativistic four-point Green functions, providing new insights into scalar field interactions and Regge trajectories.

Contribution

It presents a novel coupled system of equations for multi-channel Bethe-Salpeter problems, enabling simultaneous solutions and analytical expressions in scalar field theories.

Findings

Derived closed-form expressions for Regge trajectories.

Established sum rules and symmetry considerations.

Analyzed scalar field couplings in ladder approximation.

Abstract

A general form of multi-channel Bethe-Salpeter equation is considered. In contradistinction to the hitherto applied approaches, our coupled system of equations leads to the simultaneous solutions for all relativistic four-point Green functions (elastic and inelastic) appearing in a given theory. A set of relations which may be helpful in approximate treatments is given. An example of extracting useful information from the equations is discussed: we consider the most general trilinear coupling of N different scalar fields and obtain - in the ladder approximation - closed expressions for the Regge trajectories and their couplings to different channels in the vicinity of l = -1. Sum rules and an example containing non-obvious symmetry are discussed.