Proof of the Julia-Zee Theorem

TL;DR

This paper provides a rigorous mathematical proof of the Julia-Zee theorem, establishing that finite-energy static solutions in 2+1 dimensional classical relativistic gauge theories are necessarily electrically neutral.

Contribution

It offers the first formal proof of the Julia-Zee theorem, confirming a key principle in gauge field theory with mathematical rigor.

Findings

Finite-energy static solutions are electrically neutral.

The proof confirms the Julia-Zee theorem in a rigorous mathematical framework.

Supports the fundamental understanding of gauge field configurations in lower-dimensional spacetimes.

Abstract

It is a well accepted principle that finite-energy static solutions in the classical relativistic gauge field theory over the $(2+1)$-dimensional Minkowski spacetime must be electrically neutral. We call such a statement the Julia--Zee theorem. In this paper, we present a mathematical proof of this fundamental structural property.