Topic
Quantization (physics)
About: Quantization (physics) is a research topic. Over the lifetime, 20776 publications have been published within this topic receiving 562403 citations. The topic is also known as: quantisation.
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TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, which can be interpreted as correlators in topological open string theory.
Abstract: I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the set of equivalence classes of Poisson structures on X modulo diffeomorphisms. In fact, a more general statement is proven ("Formality conjecture"), relating the Lie superalgebra of polyvector fields on X and the Hochschild complex of the algebra of functions on X. Coefficients in explicit formulas for the deformed product can be interpreted as correlators in a topological open string theory, although I do not use explicitly the language of functional integrals. One of corollaries is a justification of the orbit method in the representation theory.
2,223 citations
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TL;DR: In this paper, it was shown that a Higgs type of Lagrangian allows for vortex-line solutions, in analogy with the vortex lines in a type II superconductor.
2,172 citations
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TL;DR: In this paper, a new mathematical framework for the Wess-Zumino chiral effective action is described, and it is shown that this action obeys an a priori quantization law, analogous to Dirac's quantization of magnetic change.
2,132 citations