Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations

TL;DR

This paper develops a non-perturbative, relativistic formalism to calculate quantum-particle scattering amplitudes, including particle-antiparticle processes, demonstrating that renormalizability is not essential for physical models.

Contribution

It introduces a three-particle formalism to derive unitary two-particle scattering amplitudes without relying on renormalization techniques.

Findings

Successfully reproduces QED results in the weak coupling limit

Demonstrates unitarity and covariance in the scattering amplitudes

Shows renormalizability is not a necessary condition for physical viability

Abstract

We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.