Lie algebra cohomology and group structure of gauge theories
- Department of Physics, Hanyang University, Seoul 133-791 (Korea)
We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar{acute e} duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator {ital Q}{sup {degree}} for the Lie algebra cohomology induced by BRST generator {ital Q}. We also point out an interesting duality relation{emdash}Poincar{acute e} duality{emdash}with respect to gauge anomalies and Wess{endash}Zumino{endash}Witten topological terms. We consider the consistent embedding of the BRST adjoint generator {ital Q}{sup {degree}} into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N{umlt o}ther charge {ital Q}{sup {degree}}. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 397456
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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