Loop representation of charged particles interacting with Maxwell and Chern-Simons fields

Details Loop representation of charged particles interacting with Maxwell and Chern-Simons fields Loop representation of charged particles interacting with Maxwell and Chern-Simons fields

2001-07-02

arxiv.org/abs/hep-th/0107013v2

Phys.Rev. D65 (2002) 065018

Physics

High Energy Physics

High Energy Physics - Theory

6 pages, improved version

Scientific paper

10.1103/PhysRevD.65.065018

The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists an unitary transformation that allows to remove the degrees of freedom associated with the paths. The existence of this transformation, which allows to make contact with the anyonic interpretation of the model, is subjected to the fact that the charge of the particles be quantized. On the other hand, in the Maxwell case, we find that charge quantization is necessary in order to the geometric representation be consistent.

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