scholarly journals Graph Complexes in Deformation Quantization

2005 ◽  
Vol 73 (3) ◽  
pp. 193-208 ◽  
Author(s):  
Domenico Fiorenza ◽  
Lucian M. Ionescu
Keyword(s):  
Deformation Quantization ◽  
Graph Complexes

scholarly journals DEFORMATION QUANTIZATION OF THE ISOTROPIC ROTATOR

1995 ◽  
Vol 10 (05) ◽  
pp. 399-407 ◽  
Author(s):  
A. STERN ◽  
I. YAKUSHIN
Keyword(s):  
Energy Spectrum ◽  
Quantum System ◽  
Chiral Symmetry ◽  
Deformation Quantization ◽  
Rigid Rotator

We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual SU (2) × SU (2) chiral symmetry, but instead [Formula: see text]. We give the energy spectrum for the resulting system.

scholarly journals KONTSEVICH'S UNIVERSAL FORMULA FOR DEFORMATION QUANTIZATION AND THE CAMPBELL–BAKER–HAUSDORFF FORMULA

2000 ◽  
Vol 11 (04) ◽  
pp. 523-551 ◽  
Author(s):  
VINAY KATHOTIA
Keyword(s):  
Lie Algebras ◽  
Deformation Quantization ◽  
Differential Operators ◽  
Main Tool ◽  
Graphical Analysis ◽  
Poisson Structures ◽  
Nilpotent Lie Algebras ◽  
Enveloping Algebra ◽  
Universal Formula ◽  
The Given

We relate a universal formula for the deformation quantization of Poisson structures (⋆-products) on ℝd proposed by Maxim Kontsevich to the Campbell–Baker–Hausdorff (CBH) formula. We show that Kontsevich's formula can be viewed as exp (P) where P is a bi-differential operator that is a deformation of the given Poisson structure. For linear Poisson structures (duals of Lie algebras) his product takes the form exp (C+L) where exp (C) is the ⋆-product given by the universal enveloping algebra via symmetrization, essentially the CBH formula. This is established by showing that the two products are identical on duals of nilpotent Lie algebras where the operator L vanishes. This completely determines part of Kontsevich's formula and leads to a new scheme for computing the CBH formula. The main tool is a graphical analysis for bi-differential operators and the computation of certain iterated integrals that yield the Bernoulli numbers.

scholarly journals Deformation Quantization, Superintegrability and Nambu Mechanics

2004 ◽  
Vol 19 (3-4) ◽  
pp. 199-203 ◽  
Author(s):  
Cosmas K. Zachos ◽  
Thomas L. Curtright
Keyword(s):  
Deformation Quantization ◽  
Nambu Mechanics

scholarly journals Two-loop part of the rational homotopy of spaces of long embeddings

2014 ◽  
Vol 23 (04) ◽  
pp. 1450018 ◽  
Author(s):  
Jim Conant ◽  
Jean Costello ◽  
Victor Turchin ◽  
Patrick Weed
Keyword(s):  
Rational Homotopy ◽  
Graph Complexes ◽  
Direct Sum

Arone and Turchin defined graph-complexes computing the rational homotopy of the spaces of long embeddings. The graph-complexes split into a direct sum by the number of loops in graphs. In this paper, we compute the homology of its two-loop part.

scholarly journals Deformation quantization of principal bundles

2016 ◽  
Vol 13 (08) ◽  
pp. 1630010
Author(s):  
Paolo Aschieri
Keyword(s):  
Quantum Group ◽  
Deformation Quantization ◽  
Principal Bundle ◽  
Base Space ◽  
Structure Group ◽  
Galois Extensions ◽  
Principal Bundles ◽  
Group Of Automorphisms ◽  
Drinfeld Twist

We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations, we obtain noncommutative principal bundles with noncommutative fiber and base space as well.

scholarly journals Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds

1993 ◽  
Vol 153 (1) ◽  
pp. 49-76 ◽  
Author(s):  
David Borthwick ◽  
Slawomir Klimek ◽  
Andrzej Lesniewski ◽  
Maurizio Rinaldi
Keyword(s):  
Deformation Quantization ◽  
Toeplitz Operators
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