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Topology of the gauge-invariant gauge field in two-color QCD | | Kurt Haller
; Lusheng Chen
; Y.S. Choi
; | | Date: |
22 Jul 1999 | | Journal: | Phys.Rev. D60 (1999) 125010 | | Subject: | hep-th hep-ph | | 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 $ell{
eq}0$, the gauge-invariant gauge field manifests winding numbers that are not integers, and are half-integers only when $ell=0$. | | Source: | arXiv, hep-th/9907176 | | Services: | Forum | Review | PDF | Favorites | |
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