Odd dimensional gauge theories and current algebra: Gerald V. Dunne and Carlo A. Trugenberger. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 80 KB
• Volume: 203
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(90)90178-q

✦ Synopsis

We quantize gauge field theories in odd dimensional space-time with actions including both a Chern-Simons term and a Yang-Mills term. Such theories will be referred to as CSYM theories. We show that there are deep connections between these theories and chiral anomalies and current algebra in even dimensional space-time. The classical canonical structure of the CSYM theories is intimately related to the algebraic properties of the consistent and covariant chiral anomalies. The quantization of the CSYM theories involves a one-cocycle which is the Wess-Zumino functional and, depending on the dimension of space-time and the gauge group, the consistent realization of gauge invariance at the quantum level imposes a quantization condition on the Chern-Simons coupling parameter. The associated cocycle behavior of physical states may be understood in terms of an Abelian functional curvature on the space of all spatial gauge fields. By considering the CSYM theories on a space-time with a spatial boundary we show that the algebra of Gauss law generators acquires a boundary-valued anomaly which is cohomologous to the Faddeev-Shatashvili proposal for the anomaly in the equal-time commutator of Gauss law operators in the theory of massless chiral fermions interacting with a gauge field in even dimensional space-time. Connections and Effective S-Matrix in Triangle Representation for Quantum Scattering.