A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

TL;DR

This paper introduces a non-perturbative integral equation method for calculating relativistic scattering amplitudes of multiple scalar particles, ensuring Lorentz invariance and unitarity without renormalization.

Contribution

It develops a set of integral equations based on Faddeev decomposition that can be extended to any finite number of particles and helicities, providing a calculable, Lorentz-invariant framework.

Findings

Equations are demonstrably calculable.

Framework reduces to non-relativistic Faddeev equations in the appropriate limit.

Method avoids renormalization and dressing of parameters.

Abstract

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require renormalization or dressing of these parameters to connect them to the boundary states.