Reduction of the Bethe-Salpeter equation for the scattering amplitude of the particles with spin 1 to system of the integral equations for invariant functions

TL;DR

This paper simplifies the Bethe-Salpeter equation for spin-1 particles into a system of integral equations for invariant functions, facilitating analysis of scattering amplitudes in relativistic quantum mechanics.

Contribution

It derives a decomposition of the scattering amplitude for spin-1 particles and transforms the Bethe-Salpeter equation into a more manageable integral equation system.

Findings

Derived the scattering amplitude decomposition using relativistic tensors

Found transformation coefficients from helicity to invariant functions

Presented an equivalent integral equation system for partial helicity amplitudes

Abstract

Bethe-Salpeter equation for the massive particles with spin 1 is considered. The scattering amplitude decomposition of the particles with spin 1 by relativistic tensors is derived. The transformation coefficients from helicity amplitudes to invariant functions is found. The integral equations system for invariant functions is obtained and partial decomposition of this system is performed. Equivalent system of the integral equation for the partial helicity amplitudes is presented.