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Nonlinear Mathematical Physics (1995), Vol.2, Nos 3--4, 247--262.

Abstract:

The paper provides a representation of canonical commutation relations (CCR) appearing in a non-Abelian gauge theory defined on a non-simply connected region in the two-dimensional Euclidean space. A necessary and sufficient condition is proven for the representation to be equivalent to the Schr\"odinger representation of CCR, and is formulated in terms of Wilson loops. Moreover, a representation inequivalent to the Schr\"odinger representation is shown to provide a mathematical expression for the non-Abelian, Aharonov-Bohm effect. Several properties of the Dirac--Weyl operator associated with the representation of CCR are also introduced. http://www.atlantis-press.com/publications/jnmp/index_jnmp.html?http%3A//www.atlantis-press.com/php/paper-details.php%3Fid%3D1061 $doi:10.2991/jnmp.1995.2.3--4.4 (how to use a DOI)$ AMS classification numbers (1991): 81S05, 81R05, 81Q05, 81Q10, 81Q60

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Open: copyright@Atlantis Press. "This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction..., provided the original work is properly cited."

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