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arXiv · 0712.0923

A Linear Equation for Wilson Loops

Poul Olesen
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Abstract

The Makeenko-Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD$_2$ it is possible to reformulate this equation as a linear equation with second order derivatives. This equation is a bound state Schrödinger equation with a three dimensional Coulomb potential. Thus, loop dynamics leads to a surprising new picture of confinement, where this phenomenon is due to a (bound state) localization in loop space, with the Wilson loops decaying exponentially outside a characteristic radius.

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Poul Olesen. 2008-02-01. A Linear Equation for Wilson Loops. https://doi.org/10.1016/j.physletb.2008.01.036

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