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arXiv · hep-th/9907176

Topology of the gauge-invariant gauge field in two-color QCD

Kurt Haller·Lusheng Chen·Y. S. Choi
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Abstract

We investigate solutions to a nonlinear integral equation which has a central role in implementing the non-Abelian Gauss's Law and in constructing gauge-invariant quark and gluon fields. Here we concern ourselves with solutions to this same equation that are not operator-valued, but are functions of spatial variables and carry spatial and SU(2) indices. We obtain an expression for the gauge-invariant gauge field in two-color QCD, define an index that we will refer to as the ``winding number'' that characterizes it, and show that this winding number is invariant to a small gauge transformation of the gauge field on which our construction of the gauge-invariant gauge field is based. We discuss the role of this gauge field in determining the winding number of the gauge-invariant gauge field. We also show that when the winding number of the gauge field is an integer $\ell{\neq}0$, the gauge-invariant gauge field manifests winding numbers that are not integers, and are half-integers only when $\ell=0$.

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Kurt Haller, Lusheng Chen, Y. S. Choi. 1999-10-19. Topology of the gauge-invariant gauge field in two-color QCD. https://doi.org/10.1103/physrevd.60.125010

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