Turkish Journal of Physics

Path Integral Quantization of the Theory of Scalar Charged Particles Interacting Via Chern-Simons Fields




De-Witt-Fadeev- Popov and the general Batalin-Fradkin-Vilkovisky approaches are used to carry out the path integral quantization of the relativistic theory of scalar charged particles interacting via Chern-Simons fields in (2+1) dimensions. Starting from the generating functional, first the path integral representation for the total many-particle Green function of the relativistic point-like charged Bose particles interacting via Chern-Simons fields in (2+1) dimensions is constructed in the form of an integral over the trajectories of the particles. It is observed that the static approximation leads to the well-known expression for the Hamiltonian for anyon interactions in (2+1) dimensions.

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