Fock Representations and Deformation Quantization of Kähler Manifolds
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DOI: 10.1007/s00006-016-0753-z
Abstract: The goal of this paper is to construct the Fock representation of noncommutative Kähler manifolds. Noncommutative Kähler manifolds studied here are constructed by deformation quantization with separation of variables, which was given by Karabegov. The… read more here.
Keywords: hler; noncommutative hler; fock representations; hler manifolds ... See more keywords
Hochschild cohomology and deformation quantization of affine toric varieties
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DOI: 10.1016/j.jalgebra.2018.03.016
Abstract: For an affine toric variety $\mathrm{Spec}(A)$, we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Under certain assumptions we compute the dimensions of the Hodge summands $T^1_{(i)}(A)$, generalizing the existing… read more here.
Keywords: affine toric; deformation quantization; affine; hochschild cohomology ... See more keywords
Deformation quantization of constrained systems: a group averaging approach
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DOI: 10.1088/1361-6382/ab6861
Abstract: Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space implementation… read more here.
Keywords: group averaging; quantization; approach; constrained systems ... See more keywords
Shifted Poisson structures and deformation quantization
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DOI: 10.1112/topo.12012
Abstract: This paper is a sequel to [PTVV]. We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and poly-vector fields. We then introduce the formalism of formal… read more here.
Keywords: poisson structures; deformation quantization; shifted poisson; structures deformation ... See more keywords