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Chern-Simons theories on the noncommutative plane.

D Bak1, K Lee, J H Park

  • 1Physics Department, University of Seoul, Seoul 130-743 Korea.

Physical Review Letters
|July 20, 2001
PubMed
Summary

Quantum mechanical consistency of U(N) Chern-Simons theories requires quantized coefficients. In U(1) theories with background charge, fractional spin is observed for charged particles and vortices.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Noncommutative geometry

Background:

  • Chern-Simons theories are fundamental in topological quantum field theory.
  • Noncommutative geometry introduces novel properties to quantum systems.
  • Understanding gauge theories on noncommutative spaces is crucial for advanced physics.

Purpose of the Study:

  • To investigate the quantum mechanical consistency of U(N) Chern-Simons theories on the noncommutative plane.
  • To determine the quantization conditions for the Chern-Simons term coefficient.
  • To analyze the spin of particles and vortices in U(1) theories with background charge.

Main Methods:

  • Analysis of U(N) Chern-Simons theories on the noncommutative plane.
  • Derivation of quantization rules for the Chern-Simons coefficient.
  • Calculation of angular momentum and particle/vortex spin.

Main Results:

  • Quantization of the Chern-Simons coefficient kappa = n/2pi for U(N) theories.
  • Modified quantization rule kappa+rho(e)straight theta = n/2pi in the presence of background charge density.
  • Determination of fractional spin 1/2n for charged particles and half-integer/integer spin -n/2 for vortices in U(1) theory.

Conclusions:

  • The study reveals essential quantization conditions for Chern-Simons theories on noncommutative spaces.
  • Fractional spin properties of particles and vortices are established in U(1) gauge theories.
  • Findings have implications for understanding topological phases and exotic quantum phenomena.

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