2023-04-02T03:37:48Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/690592022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Representation of canonical commutation relations in a gauge theory, the Aharonov-Bohm effect, and Dirac Weyl operatorArai, A.open access410We consider a representation of canonical commutation relations (CCR) appearing in a (non-Abelian) gauge theory on a non-simply connected region in the twodimensional Euclidean space. A necessary and sufficient condition for the representation to be equivalent to the Schrodinger representation of CCR is given in terms of Wilson loops. A representation inequivalent to the Schrodinger representation gives a mathematical expression for the (non-Abelian) Aharonov-Bohm effect. Some aspects of the Dirac-Weyl operator associated with the representation of CCR are discussed.Department of Mathematics, Hokkaido University1995-09-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83455http://hdl.handle.net/2115/6905910.14943/83455Hokkaido University Preprint Series in Mathematics308117https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69059/1/pre308.pdfapplication/pdf878.38 KB1995-09-01