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
- Asao ARAI
- Corresponding Author
- Asao ARAI
Available Online 19 December 2006.
- https://doi.org/10.2991/jnmp.1995.2.3-4.4How to use a DOI?
- 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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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 -