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Quantum observables, Lie algebra homology and TQFT | | Albert Schwarz
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25 Apr 1999 | | Journal: | Lett.Math.Phys. 49 (1999) 115-122 | | Subject: | hep-th | | Affiliation: | UCDavis | | 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. | | Source: | arXiv, hep-th/9904168 | | Services: | Forum | Review | PDF | Favorites | |
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