Inevitable emergence of composite gauge bosons

TL;DR

This paper proves a theorem that in gauge-invariant local matter-only theories, composite gauge bosons must form dynamically, supported by algebraic proof and diagrammatic illustration in large-N models.

Contribution

It establishes a fundamental theorem linking gauge invariance and the inevitable formation of composite gauge bosons in matter-only theories.

Findings

Theorem proven using charge-field algebra and form factor analyticity.

Composite gauge bosons emerge dynamically in matter-only gauge-invariant theories.

Diagrammatic analysis in large-N models illustrates the theorem's implications.

Abstract

A simple theorem is proved: When a gauge-invariant local field theory is written in terms of matter fields alone, a composite gauge boson or bosons must be formed dynamically. The theorem results from the fact that the Noether current vanishes in such theories. The proof is carried out by use of the charge-field algebra at equal time in the Heisenberg picture together with the well-established analyticity of the form factor of the current. While there is no need of diagram calculation for the proof, we demonstrate in the leading 1/N expansion of the existing models what the theorem means in diagrams and how the composite gauge boson emerges.