Compositeness, Bargmann-Wigner solutions within a U(1)-interaction quantum-field-theory expansion, and charge

TL;DR

This paper derives new solutions to the Bargmann-Wigner equations within a U(1) quantum field theory framework, linking fermion-antifermion pairs to vector fields satisfying Proca and Maxwell's equations, and explores implications for charge quantization and superconductivity.

Contribution

It introduces novel solutions to Bargmann-Wigner equations that connect fermion pairs to vector fields, advancing understanding of charge and superconductivity in quantum field theory.

Findings

Vector solutions satisfy Proca and Maxwell's equations.

Charge quantization is derived from vector field conditions.

Connections to QCD superconductivity and four-fermion models.

Abstract

New solutions of the Bargmann-Wigner equations are obtained: free fermion-antifermion pairs, each satisfying Dirac's equation, with parallel momenta and momenta on a plane, produce vectors satisfying Proca's equations. These equations are consistent with Dirac's and Maxwell's equations, as zero-order conditions within a Lagrangian expansion for the U(1)-symmetry quantum field theory. Such vector solutions' demand that they satisfy Maxwell's equations and quantization fix the charge. The current equates the vector field, reproducing the superconductivity London equations, thus, binding and screening conditions. The derived vertex connects to QCD superconductivity and constrains four-fermion interaction composite models.