Complex Angular Momentum Diagonalization of the Bethe-Salpeter Structure in General Quantum Field Theory

TL;DR

This paper develops a method to diagonalize the Bethe-Salpeter structure of four-point functions in quantum field theory using complex angular momentum, revealing connections to Regge poles and asymptotic behaviors.

Contribution

It introduces a diagonalization approach for the Bethe-Salpeter structure in CAM variables, linking Regge poles to the analytic framework of QFT.

Findings

Diagonalization of Bethe-Salpeter structure in CAM variables.

Existence of Regge poles with factorized residues.

Asymptotic behavior governed by Bethe-Salpeter kernel.

Abstract

The Complex Angular Momentum (CAM) representation of (scalar) four-point functions has been previously established starting from the general principles of local relativistic Quantum Field Theory (QFT). Here, we carry out the diagonalization of the general $t$-channel Bethe--Salpeter (BS) structure of four point functions in the corresponding CAM variable $\lambda_{t},$ for all negative values of the squared-energy variable $t$. This diagonalization is closely related to the existence of BS-equations for the absorptive parts in the crossed channels, interpreted as convolution equations with spectral properties. The production of Regge poles equipped with factorized residues involving Euclidean three-point functions appears as conceptually built-in in the analytic axiomatic framework of QFT. The existence of leading Reggeon terms governing the asymptotic behaviour of the four-point function at fixed $t$ is strictly conditioned by the asymptotic behaviour of a global Bethe-Salpeter kernel of the theory.