2023 Impact factor 4.2
Particles and Fields
Eur. Phys. J. C 11, 733-738
DOI 10.1007/s100529900134

The Chern-Simons term induced at high temperature and the quantization of its coefficient

Wan-Yun Zhao

Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735, Beijing 100080, P.R. China

Received: 7 April 1999 / Published online: 3 November 1999

By perturbative calculations of the high-temperature ground-state axial vector current of fermion fields coupled to gauge fields, an anomalous Chern-Simons topological mass term is induced in the three-dimensional effective action. The anomaly in three dimensions appears just in the ground-state current rather than in the divergence of ground-state current. In the Abelian case, the contribution comes only from the vacuum polarization graph, whereas in the non-Abelian case, contributions come from the vacuum polarization graph and the two triangle graphs. The relation between the quantization of the Chern-Simons coefficient and the Dirac quantization condition of magnetic charge is also obtained. It implies that in a (2+1)-dimensional QED with the Chern-Simons topological mass term and a magnetic monopole with magnetic charge g present, the Chern-Simons coefficient must be also quantized, just as in the non-Abelian case.

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