Fedosov quantization on symplectic ringed spaces
نویسندگان
چکیده
منابع مشابه
Notes on quantization of symplectic vector spaces over finite fields
In these notes we construct a quantization functor, associating an Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main technical result is a proof of a stronger form of the Stone-von Neumann theorem for the Heisenberg group over Fq. Our result ...
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A coordinate-free definition for Wick-type symbols is given for symplectic manifolds by means of the Fedosov procedure. The main ingredient of this approach is a bilinear symmetric form defined on the complexified tangent bundle of the symplectic manifold and subject to some set of algebraic and differential conditions. It is precisely the structure which describes a deviation of the Wick-type ...
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The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle T * ρ M which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The...
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A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the e...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2002
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1427411