Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-03-29
J.Math.Phys. 37 (1996) 6106-6120
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, RevTex, Revised version submitted to J. Math. Phys
Scientific paper
10.1063/1.531766
We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'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 $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e 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 N\"other charge $Q^{\dagger}$.
Lee Bum-Hoon
Yang Hyun Seok
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