Quantum observables, Lie algebra homology and TQFT

Abstract

Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha }$ where $T_{\alpha }$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{{\alpha }_1...{\alpha }_k}$ that determines a homology class of the Lie algebra $G$ the expression $c^{{\alpha }_1...{\alpha }_k}{T}_{{\alpha }_1}...T_{{\alpha }_k}$ is again a quantum observables. This theorem is used to construct quantum observables in BV sigma-model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.

arXiv comment10 pages

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