Summary
We quantize canonically the Abelian Chern-Simons theory coupled to the spinor field with and without Maxwell term in the Coulomb gauge and consider the typical form of the anyonic operators which do not rely on the presence or the absence of the Maxwell term. The gauge non-invariance of the canonical pair of the gauge field in Chern-Simons theory is crucial.
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Kim, J.K., Shin, H. On anyonic operators with and without Maxwell term. Nuov Cim B 109, 1323–1328 (1994). https://doi.org/10.1007/BF02722843
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DOI: https://doi.org/10.1007/BF02722843