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arXiv · hep-th/9503204

Lie algebra cohomology and group structure of gauge theories

Hyun Seok Yang·Bum-Hoon Lee
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Abstract

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré 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 $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincaré duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint Nöther charge $Q^{\dagger}$.

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Hyun Seok Yang, Bum-Hoon Lee. 1995-10-21. Lie algebra cohomology and group structure of gauge theories. https://doi.org/10.1063/1.531766

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