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Definition of Chern-Simons terms in thermal \(QED_3\) revisited. (English) Zbl 0927.58009

Summary: We present two compact derivations of the correct definition of the Chern-Simons term in the topologically non-trivial context of thermal \(\text{QED}_3\). One is based on a transgression descent from a \(D=4\) background connection, the other on embedding the Abelian model in \(\text{SU}(2)\). The results agree with earlier cohomology conclusions and can be also used to justify a recent simple heuristic approach. The correction to the naive Chern-Simons term, and its behavior under large gauge transformations are displayed.

MSC:

58E40 Variational aspects of group actions in infinite-dimensional spaces
81V05 Strong interaction, including quantum chromodynamics
81T13 Yang-Mills and other gauge theories in quantum field theory
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