1992/09/24 by K. Haller, Haller, K., E. Lim-Lombridas +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9209098
14pp
arxiv created 1992/09/24 · arxiv updated 2009/11/30
We discuss the canonical quantization of Chern-Simons theory in 2+1 dimensions, minimally coupled to a Dirac spinor field. Gauss's law and the gauge condition, A0 = 0, are implemented by embedding the formulation in an appropriate physical subspace. We find two kinds of charged particle states in this model. One kind has a rotational anomaly in the form of arbitrary phases that develop in 2π rotations; the other kind rotates ``normally''---i.e., charged states only change sign in 2π rotations. The rotational anomaly has nothing to do with the implementation of Gauss's law. It is possible to inadvertently produce these anomalous states in the process of implementing Gauss's law, but it is also possible to implement Gauss's law without producing rotational anomalies. Moreover, states with or without rotational anomalies obey ordinary Fermi statistics.