Abstract
We consider one type of gauge-invariant anyon operators from the complex scalar field theory minimally coupled to the Chern-Simons term in 2+1 dimensions. In the Coulomb gauge condition, the anyonicity of operators, the multi-valued states, and the spin-statistics relation are derived by considering the proper distribution function, which appears in the definition of anyon operators. It is shown that the anyonicity is not a gauge artifact by also obtaining it in the covariant gauge.
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