Static Solution in Source-Free SU(2) Yang-Mills Theory

TL;DR

This paper demonstrates the existence of a stable, finite-energy, static soliton solution in source-free SU(2) Yang-Mills theory, challenging the notion that such solutions require sources and highlighting the role of topological effects.

Contribution

It presents the first static, non-singular, source-free SU(2) Yang-Mills solution in four-dimensional Minkowski space, revealing new topological and stability properties.

Findings

Existence of a stable, finite-energy soliton in source-free SU(2) Yang-Mills theory.

The solution is characterized by non-trivial topology and an imaginary $A_0^a$ component.

The solution has a hermitian Hamilton and positive energy.

Abstract

We show that a non-trivial topological effect breaks the conformal invariance of pure Yang-Mills theory. Thus it is possible that classic particle-like solutions exists in pure non-Abelian Yang-Mills theory. We find a static, non-singular solution in source-free SU(2) Yang-Mills theory in four-dimensional Minkowski space. This solution is a stable soliton characterized by non-trivial topology and imaginary $A_0^a$, i.e., $A_0^aA_0^a<0$. It yields hermitian Hamilton, and finite, positive energy.