Journal of Nonlinear Mathematical Physics

Volume 2, Issue 3-4, September 1995, Pages 247 - 262

Representation of Canonical Commutation Relations in a Gauge Theory, the Aharonov-Bohm Effect, and the Dirac-Weyl Operator

Authors
Asao ARAI
Corresponding Author
Asao ARAI
Available Online 19 December 2006.
DOI
https://doi.org/10.2991/jnmp.1995.2.3-4.4How to use a DOI?
Abstract
We consider a representation of canonical commutation relations (CCR) appearing in a (non-Abelian) gauge theory on a non-simply connected region in the two-dimensional Euclidean space. A necessary and sufficient condition for the representation to be equivalent to the Schrödinger representation of CCR is given in terms of Wilson loops. A representation inequivalent to the Schrödinger representation gives a mathematical expression for the (non-Abelian) Aharonov-Bohm effect. Some aspects of the DiracWeyl operator associated with the representation of CCR are discussed.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
2 - 3
Pages
247 - 262
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1995.2.3-4.4How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Asao ARAI
PY  - 2006
DA  - 2006/12
TI  - Representation of Canonical Commutation Relations in a Gauge Theory, the Aharonov-Bohm Effect, and the Dirac-Weyl Operator
JO  - Journal of Nonlinear Mathematical Physics
SP  - 247
EP  - 262
VL  - 2
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.3-4.4
DO  - https://doi.org/10.2991/jnmp.1995.2.3-4.4
ID  - ARAI2006
ER  -