Effect of rotation symmetry to abelian Chern-Simons field theory and anyon equation on a sphere

Details Effect of rotation symmetry to abelian Chern-Simons field theory and anyon equation on a sphere Effect of rotation symmetry to abelian Chern-Simons field theory and anyon equation on a sphere

1994-07-09

arxiv.org/abs/hep-th/9407048v1

Phys.Rev.D50:5241-5251,1994

Physics

High Energy Physics

High Energy Physics - Theory

Revtex 25pages

Scientific paper

10.1103/PhysRevD.50.5241

We analyze the Chern-Simons field theory coupled to non-relativistic matter field on a sphere using canonical transformation on the fields with special attention to the role of the rotation symmetry: SO(3) invariance restricts the Hilbert space to the one with a definite number of charges and dictates Dirac quantization condition to the Chern-Simons coefficient, whereas SO(2) invariance does not. The corresponding Schr\"odinger equation for many anyons (and for multispecies) on the sphere are presented with appropriate boundary condition. In the presence of an external magnetic monopole source, the ground state solutions of anyons are compared with monopole harmonics. The role of the translation and modular symmetry on a torus is also expounded.

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