Abstract:We study the gauge invariant dynamically conserved charges, and their corresponding densities, for instanton solutions of Yang-Mills theories in four dimensional Euclidean space, for the gauge group SU(2). Those charges were constructed in [1,2] through the integral equations of Yang-Mills theory, using techniques on generalized loop spaces. We use the integral non-Abelian Gauss law to evaluate the gauge-invariant flux of the magnetic and electric non-abelian fields through spherical surfaces centered at origin of the instanton solution. From such a flux, we define gauge-invariant charge densities by considering the charge within an infinitesimal spherical shell of radius $r$. We discuss the issue of the reparameterization invariance of the charges and densities, and show that the magnetic and electric fluxes for the instanton and anti-instanton, at the Euclidean time $x^4 = 0$ and radius $r=1$, which here corresponds to the size $\lambda$ of those solutions, are non-zero and observable. Our results give an interesting picture of the internal structure of the instanton, and may be important for the properties of the Yang-Mills $\theta$-vacuum.
From: Luiz Agostinho Ferreira [view email]
[v1]
Fri, 12 Jun 2026 17:05:39 UTC (1,100 KB)
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