Relevant bibliographies by topics / Geometric quantization

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

Academic literature on the topic 'Geometric quantization'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Geometric quantization"

1

Camosso, Simone. "Prequantization, Geometric Quantization, Corrected Geometric Quantization." Journal of Applied Mathematics and Physics 09, no. 09 (2021): 2290–320. http://dx.doi.org/10.4236/jamp.2021.99146.

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Gracia‐Bondía, José M., and Joseph C. Várilly. "From geometric quantization to Moyal quantization." Journal of Mathematical Physics 36, no. 6 (1995): 2691–701. http://dx.doi.org/10.1063/1.531059.

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Paradan, Paul-Émile. "Formal geometric quantization." Annales de l’institut Fourier 59, no. 1 (2009): 199–238. http://dx.doi.org/10.5802/aif.2429.

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ALI, S. TWAREQUE, and MIROSLAV ENGLIŠ. "QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS." Reviews in Mathematical Physics 17, no. 04 (2005): 391–490. http://dx.doi.org/10.1142/s0129055x05002376.

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This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics, Segal and Borel quantizations, geometric quantization, various ramifications of deformation quantization, Berezin and Berezin–Toeplitz quantizations, prime quantization and coherent state quantization. We have attempted to give an account sufficiently in depth to convey the general picture, as well as to indicate the mutual relationshi
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ABRIKOSOV, A. A., E. GOZZI, and D. MAURO. "TIME AND GEOMETRIC QUANTIZATION." Modern Physics Letters A 18, no. 33n35 (2003): 2347–54. http://dx.doi.org/10.1142/s0217732303012568.

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In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.
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Śniatycki, Jędrzej. "Lectures on Geometric Quantization." Geometry, Integrability and Quantization 17 (2016): 95–129. http://dx.doi.org/10.7546/giq-17-2016-95-129.

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Rota, Gian-Carlo. "Geometric quantization in action." Advances in Mathematics 58, no. 3 (1985): 322. http://dx.doi.org/10.1016/0001-8708(85)90128-8.

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Mykytyuk, I. V., and A. K. Prykarpats'kyy. "Reduction and geometric quantization." Ukrainian Mathematical Journal 44, no. 9 (1992): 1116–22. http://dx.doi.org/10.1007/bf01058372.

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Paradan, Paul-Émile. "Formal geometric quantization II." Pacific Journal of Mathematics 253, no. 1 (2011): 169–211. http://dx.doi.org/10.2140/pjm.2011.253.169.

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Bordemann, Martin, Jens Hoppe, Peter Schaller, and Martin Schlichenmaier. "gl(∞) and geometric quantization." Communications in Mathematical Physics 138, no. 2 (1991): 209–44. http://dx.doi.org/10.1007/bf02099490.

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Dissertations / Theses on the topic "Geometric quantization"

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Gardell, Fredrik. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296618.

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In this project we introduce the general idea of geometric quantization and demonstratehow to apply the process on a few examples. We discuss how to construct a line bundleover the symplectic manifold with Dirac’s quantization conditions and how to determine if we are able to quantize a system with the help of Weil’s integrability condition. To reducethe prequantum line bundle we employ real polarization such that the system does notbreak Heisenberg’s uncertainty principle anymore. From the prequantum bundle and thepolarization we construct the sought after Hilbert space.
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Hedlund, William. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325649.

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We formulate a process of quantization of classical mechanics, from a symplecticperspective. The Dirac quantization axioms are stated, and a satisfactory prequantizationmap is constructed using a complex line bundle. Using polarization, it isdetermined which prequantum states and observables can be fully quantized. Themathematical concepts of symplectic geometry, fibre bundles, and distributions are exposedto the degree to which they occur in the quantization process. Quantizationsof a cotangent bundle and a sphere are described, using real and K¨ahler polarizations,respectively.
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Robson, Mark Andrew. "Geometric quantization of constrained systems." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363252.

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Flude, James Paul Maurice. "Geometric asymptotics of spin." Thesis, University of Nottingham, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285637.

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Hsu, Siu-fai, and 許紹輝. "Geometric quantization of fermions and complex bosons." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50434500.

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Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible. In quantum field theory, charge conjungation can be defined on complex
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Terizakis, George. "Geometric quantization, symplectic reduction and singular polarizations." Thesis, University of Warwick, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300225.

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Castañeda, Terrones Jose Luis. "Review of geometric quantization and WKB method." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/157267.

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Submitted by Jose Luis Castañeda Terrones (joseluiscastanedat@gmail.com) on 2018-09-26T18:09:17Z No. of bitstreams: 1 Tese Jose Castaneda Final.pdf: 575058 bytes, checksum: 286cdeb9575d9c271e1d873096c5ad93 (MD5)<br>Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-10-09T14:26:09Z (GMT) No. of bitstreams: 1 castanedaterrones_js_me_ift.pdf: 18481 bytes, checksum: e7b453cf971ef08437a1e5e5f83e4380 (MD5)<br>Made available in DSpace on 2018-10-09T14:26:09Z (GMT). No. of bitstreams: 1 castanedaterrones_js_me_ift.pdf: 18481 bytes, checksum: e7b453cf971ef08437a1e5
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Pinto, J. A. "Some aspects of geometric quantization and their physical basis." Thesis, University of St Andrews, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377329.

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Sulcs, Sue 1952. "Maxwellian Renaissance and the illusion of quantization." Monash University, School of Philosophy and Bioethics, 2002. http://arrow.monash.edu.au/hdl/1959.1/8536.

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Rubinstein, Yanir Akiva. "Geometric quantization and dynamical constructions on the space of Kähler metrics." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44270.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>Includes bibliographical references (p. 185-200).<br>This Thesis is concerned with the study of the geometry and structure of the space of Kihler metrics representing a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a problem of geometric quantization: Can the geometry of the infinite-dimensional space of Kähler metrics be approximated in terms of the geometry of the finite-dimensional spaces of FubiniStudy Bergman metrics sitting inside it? We restrict to
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Books on the topic "Geometric quantization"

1

Woodhouse, Nicholas. Geometric quantization. 2nd ed. Clarendon Press, 1991.

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Klauder, John R. Beyond conventional quantization. Cambridge University Press, 2000.

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Pierre, Antoine Jean, and Workshop on Geometric Methods in Physics (12th : 1993 : Białowieża, Województwo Podlaskie, Poland), eds. Quantization and infinite-dimensional systems. Plenum Press, 1994.

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Puta, Mircea. Hamiltonian Mechanical Systems and Geometric Quantization. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1992-4.

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Puta, Mircea. Hamiltonian mechanical systems and geometric quantization. Kluwer Academic Publishers, 1993.

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Puta, Mircea. Old and new aspects of geometric quantization. Tipografia Universității din Timișoara, 1986.

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Brylinski, Jean-Luc. Loop Spaces, Characteristic Classes and Geometric Quantization. Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-0-8176-4731-5.

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Brylinski, J. L. Loop spaces, characteristic classes, and geometric quantization. Birkhauser, 1993.

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Bandyopadhyay, Pratul. Geometry, topology, and quantization. Kluwer Academic Publishers, 1996.

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P, Landsman N., Pflaum M, and Schlichenmaier Martin 1952-, eds. Quantization of singular symplectic quotients. Birkhäuser Verlag, 2001.

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Book chapters on the topic "Geometric quantization"

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Puta, Mircea. "Geometric Quantization." In Hamiltonian Mechanical Systems and Geometric Quantization. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1992-4_7.

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Kirillov, A. A. "Geometric Quantization." In Dynamical Systems IV. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-06791-8_2.

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Kirillov, A. A. "Geometric Quantization." In Dynamical Systems IV. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-06793-2_2.

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Souriau, Jean-Marie. "Geometric quantization." In Structure of Dynamical Systems. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0281-3_18.

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Cordani, Bruno. "Geometric Quantization." In The Kepler Problem. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8051-0_9.

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Nair, V. Parameswaran. "Geometric Quantization." In SpringerBriefs in Physics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65801-3_4.

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Guillemin, Victor, Viktor Ginzburg, and Yael Karshon. "Geometric quantization." In Moment Maps, Cobordisms, and Hamiltonian Group Actions. American Mathematical Society, 2002. http://dx.doi.org/10.1090/surv/098/06.

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Dwivedi, Shubham, Jonathan Herman, Lisa C. Jeffrey, and Theo van den Hurk. "Geometric Quantization." In SpringerBriefs in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27227-2_11.

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Awane, Azzouz, and Michel Goze. "Geometric Pre-Quantization." In Pfaffian Systems, k-Symplectic Systems. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9526-1_9.

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Puta, Mircea. "Geometric Prequantization." In Hamiltonian Mechanical Systems and Geometric Quantization. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1992-4_6.

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Conference papers on the topic "Geometric quantization"

1

Rios, P. de M., G. M. Tuynman, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Weyl Quantization from geometric quantization." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043868.

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Sergeev, Armen, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "On Quantization of Universal Teichmüller Space." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043873.

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ROSENSTEEL, G., and E. IHRIG. "GEOMETRIC QUANTIZATION OF RIEMANN ROTORS." In Proceedings of XI Workshop on Geometric Methods in Physics. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814440844_0004.

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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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Wernli, Konstantin. "Six lectures on geometric quantization." In Modave Summer School in Mathematical Physics. Sissa Medialab, 2023. http://dx.doi.org/10.22323/1.435.0005.

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Bates, Larry, Richard Cushman, Mark Hamilton, et al. "Decomposition of the Quantization Representation of an SU(2) Action." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043871.

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Ma, Xiaonan. "Geometric Quantization on Kähler and Symplectic Manifolds." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0074.

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Tosiek, J., Piotr Kielanowski, Victor Buchstaber, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Fedosov Deformation Quantization with some Family of Compatible Symplectic Connections." In XXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS. AIP, 2010. http://dx.doi.org/10.1063/1.3527413.

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MLADENOV, IVAILO M., and VASIL V. TSANOV. "GROUP REPRESENTATIONS AND QUANTIZATION OF THE MOMENTUM MAP." In Proceedings of XI Workshop on Geometric Methods in Physics. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814440844_0002.

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Ma, Xiaonan, and Weiping Zhang. "Toeplitz Quantization and Symplectic Reduction." In Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772527_0029.

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Reports on the topic "Geometric quantization"

1

Holod, Petro I. Geometric Quantization, Cohomology Groups and Intertwining Operators. GIQ, 2012. http://dx.doi.org/10.7546/giq-1-2000-95-104.

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Sansonetto, Nicola. Monodromy and the Bohr-Sommerfeld Geometric Quantization. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-320-328.

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Sansonetto, Nicola. Monodromy and the Bohr-Sommerfeld Geometric Quantization. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-20-2010-97-106.

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Grigorescu, Marius. Geometrical Framework of Quantization Problem. GIQ, 2012. http://dx.doi.org/10.7546/jgsp-23-2011-1-27.

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