The Resource Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, (electronic resource)
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, (electronic resource)
 Summary
 This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a noncommutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch.   The purely algebraic approaches given in the previous chapters do not take the geometry of spacetime into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved spacetime, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to noncommutativity. An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the BatalinVilkovisky formalism and direct products of spectral triples. This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory
 Language
 eng
 Extent
 X, 341 p. 6 illus.
 Contents

 Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.))
 General Overview (Alexander Cardona, Sylvie Paycha and Andrés F. Reyes Lega)
 Introduction
 Poisson Geometry and Classical Dynamics
 Geometric and Deformation Quantization
 Noncommutative Geometry and Quantum Groups
 Deformation Quantization and Group Actions (Simone Gutt)
 What do we mean by quantization?
 Deformation Quantization
 Fedosov{u2019}s star products on a symplectic manifold
 Classification of Poisson deformations and star products
 Star products on Poisson manifolds and formality
 Group actions in deformation quantization
 Reduction in deformation quantization
 Some remarks about convergence
 . Principal fiber bundles in noncommutative geometry (Christian Kassel)
 Introduction
 Review of principal fiber bundles
 Basic ideas of noncommutative geometry
 From groups to Hopf algebras
 Quantum groups associated with SL2(C)
 Group actions in noncommutative geometry
 Hopf Galois extensions
 Flat deformations of Hopf algebras
 An Introduction to Nichols Algebras (Nicolás Andruskiewitsch)
 Preliminaries
 Braided tensor categories
 Nichols algebras
 Classes of Nichols algebras
 Quantum Field Theory in Curved SpaceTime (Andrés F. Reyes Lega)
 Introduction
 Quantum Field Theory in Minkowski SpaceTime
 Quantum Field Theory in Curved SpaceTime
 Cosmology
 An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez)
 Introduction
 Particle and Superparticle
 Pure Spinor Superstring
 Appendix
 Introduction to Elliptic Fibrations (Mboyo Esole)
 Introduction
 Elliptic curves over C
 Elliptic fibrations
 KodairaNéron classification of singular fibers
 Miranda models
 Batalin{u2013}Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen)
 Motivations and program
 BV integral
 Gauge fixing
 Master equations
 Conclusion
 Split ChernSimons theory in the BVBFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli)
 Introduction
 Overview of the BV and BVBFV formalisms
 ChernSimons theory as a BFlike theory
 Split ChernSimons theory on the solid torus
 Conclusions and outlook
 Weighted direct product of spectral triples (Kevin Falk)
 Introduction and motivation. Weighted direct product of spectral triples
 Example of weighted direct product with Toeplitz operators
 Index
 Isbn
 9783319654270
 Label
 Quantization, Geometry and Noncommutative Structures in Mathematics and Physics
 Title
 Quantization, Geometry and Noncommutative Structures in Mathematics and Physics
 Statement of responsibility
 edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega
 Language
 eng
 Summary
 This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a noncommutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch.   The purely algebraic approaches given in the previous chapters do not take the geometry of spacetime into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved spacetime, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to noncommutativity. An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the BatalinVilkovisky formalism and direct products of spectral triples. This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory
 Image bit depth
 0
 Literary form
 non fiction
 Series statement
 Mathematical Physics Studies,
 Label
 Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.))  General Overview (Alexander Cardona, Sylvie Paycha and Andrés F. Reyes Lega)  Introduction  Poisson Geometry and Classical Dynamics  Geometric and Deformation Quantization  Noncommutative Geometry and Quantum Groups  Deformation Quantization and Group Actions (Simone Gutt)  What do we mean by quantization?  Deformation Quantization  Fedosov{u2019}s star products on a symplectic manifold  Classification of Poisson deformations and star products  Star products on Poisson manifolds and formality  Group actions in deformation quantization  Reduction in deformation quantization  Some remarks about convergence  . Principal fiber bundles in noncommutative geometry (Christian Kassel)  Introduction  Review of principal fiber bundles  Basic ideas of noncommutative geometry  From groups to Hopf algebras  Quantum groups associated with SL2(C)  Group actions in noncommutative geometry  Hopf Galois extensions  Flat deformations of Hopf algebras  An Introduction to Nichols Algebras (Nicolás Andruskiewitsch)  Preliminaries  Braided tensor categories  Nichols algebras  Classes of Nichols algebras  Quantum Field Theory in Curved SpaceTime (Andrés F. Reyes Lega)  Introduction  Quantum Field Theory in Minkowski SpaceTime  Quantum Field Theory in Curved SpaceTime  Cosmology  An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez)  Introduction  Particle and Superparticle  Pure Spinor Superstring  Appendix  Introduction to Elliptic Fibrations (Mboyo Esole)  Introduction  Elliptic curves over C  Elliptic fibrations  KodairaNéron classification of singular fibers  Miranda models  Batalin{u2013}Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen)  Motivations and program  BV integral  Gauge fixing  Master equations  Conclusion  Split ChernSimons theory in the BVBFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli)  Introduction  Overview of the BV and BVBFV formalisms  ChernSimons theory as a BFlike theory  Split ChernSimons theory on the solid torus  Conclusions and outlook  Weighted direct product of spectral triples (Kevin Falk)  Introduction and motivation. Weighted direct product of spectral triples  Example of weighted direct product with Toeplitz operators  Index
 http://library.link/vocab/cover_art
 https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9783319654270&userID=ebscotest&password=ebscotest
 Dimensions
 unknown
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4379952'}
 Extent
 X, 341 p. 6 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319654270
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
Embed (Experimental)
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/QuantizationGeometryandNoncommutative/5Z458LhyVRs/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/QuantizationGeometryandNoncommutative/5Z458LhyVRs/">Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, (electronic resource)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/QuantizationGeometryandNoncommutative/5Z458LhyVRs/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/QuantizationGeometryandNoncommutative/5Z458LhyVRs/">Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega, (electronic resource)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>