Relevant bibliographies by topics / Equivariant quantization

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Equivariant quantization'

Author: Grafiati
Published: 16 November 2024

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Journal articles on the topic "Equivariant quantization"

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Bieliavsky, Pierre, Victor Gayral, Sergey Neshveyev, and Lars Tuset. "On deformations of C∗-algebras by actions of Kählerian Lie groups." International Journal of Mathematics 27, no. 03 (March 2016): 1650023. http://dx.doi.org/10.1142/s0129167x16500233.

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We show that two approaches to equivariant strict deformation quantization of C[Formula: see text]-algebras by actions of negatively curved Kählerian Lie groups, one based on oscillatory integrals and the other on quantizations maps defined by dual 2-cocycles, are equivalent.
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Lecomte, Pierre B. A. "Towards Projectively Equivariant Quantization." Progress of Theoretical Physics Supplement 144 (December 1, 2001): 125–32. http://dx.doi.org/10.1143/ptps.144.125.

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Poncin, N., F. Radoux, and R. Wolak. "Equivariant quantization of orbifolds." Journal of Geometry and Physics 60, no. 9 (September 2010): 1103–11. http://dx.doi.org/10.1016/j.geomphys.2010.04.003.

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PFLAUM, M. J., H. B. POSTHUMA, X. TANG, and H. H. TSENG. "ORBIFOLD CUP PRODUCTS AND RING STRUCTURES ON HOCHSCHILD COHOMOLOGIES." Communications in Contemporary Mathematics 13, no. 01 (February 2011): 123–82. http://dx.doi.org/10.1142/s0219199711004142.

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In this paper, we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case, the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an S1-equivariant version of the Chen–Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology.
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Hawkins, Eli. "Quantization of Equivariant Vector Bundles." Communications in Mathematical Physics 202, no. 3 (May 1, 1999): 517–46. http://dx.doi.org/10.1007/s002200050594.

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Tang, Xiang, and Yi-Jun Yao. "K -theory of equivariant quantization." Journal of Functional Analysis 266, no. 2 (January 2014): 478–86. http://dx.doi.org/10.1016/j.jfa.2013.10.005.

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Rogers, Alice. "Equivariant BRST quantization and reducible symmetries." Journal of Physics A: Mathematical and Theoretical 40, no. 17 (April 11, 2007): 4649–63. http://dx.doi.org/10.1088/1751-8113/40/17/016.

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Michel, Jean-Philippe. "Conformally Equivariant Quantization for Spinning Particles." Communications in Mathematical Physics 333, no. 1 (December 16, 2014): 261–98. http://dx.doi.org/10.1007/s00220-014-2229-0.

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Duval, Christian, Pierre Lecomte, and Valentin Ovsienko. "Conformally equivariant quantization: existence and uniqueness." Annales de l’institut Fourier 49, no. 6 (1999): 1999–2029. http://dx.doi.org/10.5802/aif.1744.

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Donin, J., and A. Mudrov. "Reflection equation, twist, and equivariant quantization." Israel Journal of Mathematics 136, no. 1 (December 2003): 11–28. http://dx.doi.org/10.1007/bf02807191.

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Dissertations / Theses on the topic "Equivariant quantization"

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Tizzano, Luigi. "Geometry of BV quantization and Mathai-Quillen formalism." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5941/.

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Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.
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Marie, Valentin. "représentations projectives et groupes quantiques localement compacts." Electronic Thesis or Diss., Reims, 2024. http://www.theses.fr/2024REIMS012.

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Cette thèse exploite un résultat de De Commer pour produire des groupes quantiques localement compacts (au sens des algèbres de von Neumann) à partir d'un groupe classique. Il s'agit de déformer la bigèbre de von Neumann d'un groupe localement compact à l'aide d'un opérateur de convolution (2-cocycle dual unitaire). L'objectif principal de cette thèse est de construire de tels 2-cocycles duaux, en généralisant au cas des représentations projectives un articlede Bieliavsky, Gayral, Neshveyev, Tuset.Les groupes nous intéressant sont des produits semi-directs devant vérifier la condition dite d'orbite duale et ayant une cohomologie non triviale en degré 2.On construit une quantification de type Kohn-Nirenberg à partir d'une représentation projective. Le star-produit de cette quantification nous permet de formuler un 2-cocycle dual naïf. On obtient une construction rigoureuse de ce 2-cocycle dual en introduisant un G-objet Galois.On exprime ensuite l'unitaire multiplicatif du groupe quantique induit par le 2-cocycle dual. En utilisant un résultat de Baaj et Skandalis sur les transformations pentagonales, on obtient à partir de l'unitaire multiplicatif que ce groupe quantique est isomorphe à un produit bicroisé twisté.L'unitaire multiplicatif induit une cohomologie dite pentagonale, et un morphisme de groupes permettant de la décrire en partie. On étudie ce morphisme.On propose un cadre altérant la condition d'orbite duale, pour étudier une quantification de type Weyl construite à l'aide de la même représentation.On présente enfin l'exemple d'un 2-cocycle dual proposé par Jondreville. On exprime l'unitaire multiplicatif du groupe quantique induit par ce 2-cocycle dual
This thesis exploits a result by De Commer to produce locally compact quantum groups (in the sense of von Neumann algebras) from a classical group. It involves deforming the von Neumann bialgebra of a locally compact group using a unitary dual 2-cocycle. The main objective of this thesis is to construct such dual 2-cocycles, by generalizing to the case of projective representations an article byBieliavsky, Gayral, Neshveyev, Tuset.The groups of interest to us are semidirect products that must satisfy the so-called dual orbit condition and have a non-trivial cohomology in degree 2. We construct a Kohn-Nirenberg type quantization from a projective representation. The star-product of this quantization allows us to formulate a naive dual 2-cocycle. We achieve a rigorous construction of this dual 2-cocycle by introducing a G-Galois object.We then express the multiplicative unitary of the quantum group induced by the dual 2-cocycle. By applying a result of Baaj and Skandalis on pentagonal transformations, we obtain from the multiplicative unitary that this quantum group is isomorphic to a cocycle bicrossed product. The multiplicative unitary induces a so-called pentagonal cohomology and a group morphism that partially describes this cohomology. We study this morphism.We then propose a setup altering the dual orbit condition, in order to study a Weyl type quantization constructed using the same representation. Finally, we present the example of a dual 2-cocycle proposed by Jondreville. We express the multiplicative unitary of the quantum group induced by this dual 2-cocycle
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Fitzpatrick, Daniel. "Almost CR Quantization via the Index of Transversally Elliptic Dirac Operators." Thesis, 2009. http://hdl.handle.net/1807/19033.

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Let $M$ be a smooth compact manifold equipped with a co-oriented subbundle $E\subset TM$. We suppose that a compact Lie group $G$ acts on $M$ preserving $E$, such that the $G$-orbits are transverse to $E$. If the fibres of $E$ are equipped with a complex structure then it is possible to construct a $G$-invariant Dirac operator $\dirac$ in terms of the resulting almost CR structure. We show that there is a canonical equivariant differential form with generalized coefficients $\mathcal{J}(E,X)$ defined on $M$ that depends only on the $G$-action and the co-oriented subbundle $E$. Moreover, the group action is such that $\dirac$ is a $G$-transversally elliptic operator in the sense of Atiyah \cite{AT}. Its index is thus defined as a generalized function on $G$. Beginning with the equivariant index formula of Paradan and Vergne \cite{PV3}, we obtain an index formula for $\dirac$ computed as an integral over $M$ that is free of choices and growth conditions. This formula necessarily involves equivariant differential forms with generalized coefficients and we show that the only such form required is the canonical form $\mathcal{J}(E,X)$. In certain cases the index of $\dirac$ can be interpreted in terms of a CR analogue of the space of holomorphic sections, allowing us to view our index formula as a character formula for the $G$-equivariant quantization of the almost CR manifold $(M,E)$. In particular, we obtain the ``almost CR'' quantization of a contact manifold, in a manner directly analogous to the almost complex quantization of a symplectic manifold.
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Books on the topic "Equivariant quantization"

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Argentina) Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry (3rd 2010 Buenos Aires. Topics in noncommutative geometry: Third Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26-August 6, 2010. Edited by Cortiñas, Guillermo, editor of compilation. Providence, RI: American Mathematical Society, 2012.

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The [ Gamma]-equivariant form of the Berezin quantization of the upper half plane. Providence, R.I: American Mathematical Society, 1998.

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Book chapters on the topic "Equivariant quantization"

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Duval, Christian, Pierre B. A. Lecomte, and Valentin Ovsienko. "Methods of Equivariant Quantization." In Noncommutative Differential Geometry and Its Applications to Physics, 1–12. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0704-7_1.

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Vergne, Michèle. "Geometric Quantization and Equivariant Cohomology." In First European Congress of Mathematics Paris, July 6–10, 1992, 249–95. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-9328-2_8.

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Vergne, Michèle. "Geometric Quantization and Equivariant Cohomology." In First European Congress of Mathematics, 249–95. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-9110-3_8.

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Matsuura, Shun, and Hiroshi Kurata. "Statistical Estimation of Quantization for Probability Distributions: Best Equivariant Estimator of Principal Points." In Machine Learning, Optimization, and Data Science, 430–41. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95467-3_31.

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Conference papers on the topic "Equivariant quantization"

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Michel, J. Ph, Piotr Kielanowski, Victor Buchstaber, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Equivariant Quantization of Spin Systems." In XXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS. AIP, 2010. http://dx.doi.org/10.1063/1.3527405.

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Shin, Woncheol, Gyubok Lee, Jiyoung Lee, Eunyi Lyou, Joonseok Lee, and Edward Choi. "Exploration Into Translation-Equivariant Image Quantization." In ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023. http://dx.doi.org/10.1109/icassp49357.2023.10096052.

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Bouwknegt, Peter, Alan Carey, and Rishni Ratnam. "Recent Advances in the Study of the Equivariant Brauer Group." In Proceedings of the Noncommutative Geometry and Physics 2008, on K-Theory and D-Branes & Proceedings of the RIMS Thematic Year 2010 on Perspectives in Deformation Quantization and Noncommutative Geometry. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814425018_0012.

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