Deformation quantization of gerbes
نویسندگان
چکیده
منابع مشابه
Deformation Quantization of Gerbes
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 ref.[1], Schwinger terms in hamiltonian quantization of chiral fermions coupled to vector potentials were computed, using some ideas from the theory of gerbes, with the help of the family index theorem for a manifold with boundary. Here, we generalize this method to include gravitational Schwinger terms.
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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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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: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2007.02.002