Deformation quantization of the heisenberg group
نویسندگان
چکیده
منابع مشابه
Deformation Quantization
1. INTRODUCTION Quantum mechanics is often distinguished from classical mechanics by a statement to the effect that the observables in quantum mechanics, unlike those in classical mechanics, do not commute with one another. Yet classical mechanics is meant to give a description (with less precision) of the same physical world as is described by quantum mechanics. One mathematical transcription ...
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0.1. In this paper we construct a number of geometrically meaningful 1– and 2– cocycles of infinite dimensional Lie groups and Lie algebras. The groups are groups of diffeomorphisms of smooth manifolds and their subgroups, such as the group of symplectomorphisms of a symplectic manifold; the Lie algebras are algebras of vector fields. Coefficient spaces of the cocycles are spaces of various ten...
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This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We als...
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In this note we give an algebraic proof of “deformation quantization” by making use of the theory of Unital Gröbner bases over a valuation ring. MSC: 16Z05,13P10 In this note we give an algebraic proof of deformation quantization (c.f. [7]). We do this be developing in (Sec. 1) the theory of unital Gröbner bases over a valuation ring. We then in (Sec. 2) obtain, almost immediately, our desired ...
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I was asked by the organisers to present some aspects of Deformation Quantization. Moshé has pursued, for more than 25 years, a research program based on the idea that physics progresses in stages, and one goes from one level of the theory to the next one by a deformation, in the mathematical sense of the word, to be defined in an appropriate category. His study of deformation theory applied to...
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ژورنال
عنوان ژورنال: Czechoslovak Journal of Physics
سال: 1994
ISSN: 0011-4626,1572-9486
DOI: 10.1007/bf01690451