Quantization, geometry and noncommutative structures in mathematics and physics. ([2017])

• Record Type: Book
• Further Information: Note: Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andres F. Reyes Lega, editors.
• Editors: Cardona, Alexander; Morales, Pedro; Ocampo, Hernan; Paycha, Sylvie; Reyes-Lega, Andrés F, 1973-
• Contents: ""Preface""; ""Contents""; ""Contributors""; ""1 Prelude: A General Overview""; ""1.1 Introduction""; ""1.2 Poisson Geometry and Classical Dynamics""; ""1.3 Geometric and Deformation Quantization""; ""1.3.1 Geometric Quantization""; ""1.3.2 Deformation Quantization""; ""1.4 Non-commutative Geometry and Quantum Groups""; ""1.5 Quantum Fields""; ""References""; ""2 Deformation Quantization and Group Actions""; ""2.1 What Do We Mean by Quantization?""; ""2.1.1 Classical Mechanics""; ""2.1.2 Quantum Mechanics""; ""2.2 Deformation Quantization""; ""2.2.1 Definition and Examples of Star Products"" ""2.2.2 Existence of Star Products""""2.2.3 The Notion of States""; ""2.3 Fedosov's Star Products on a Symplectic Manifold""; ""2.3.1 The Weyl Bundle""; ""2.3.2 Flat Connections on the Weyl Bundle""; ""2.3.3 Fedosov's Star Products""; ""2.4 Classification of Poisson Deformations and Star Products""; ""2.4.1 Hochschild Cohomology""; ""2.4.2 Equivalence of Star Products""; ""2.5 Star Products on Poisson Manifolds and Formality""; ""2.5.1 The DGLA of Polydifferential Operators""; ""2.5.2 The DGLA of Multivector Fields ""; ""2.5.3 Linfty-Algebras, Linfty-Morphism and Formality"" ""2.5.4 Formality for mathbbRd""""2.6 Group Actions in Deformation Quantization""; ""2.6.1 In a Classical Setting""; ""2.6.2 In the Deformation Quantization Setting""; ""2.6.3 Classification of Invariant Star Products""; ""2.6.4 Invariance of Fedosov's Star Product""; ""2.7 Reduction in Deformation Quantization""; ""2.7.1 The Classical Koszul Resolution""; ""2.7.2 The Quantized Koszul Complex""; ""2.7.3 The Reduced Star Product""; ""2.8 Some Remarks About Convergence""; ""References""; ""3 Principal Fiber Bundles in Non-commutative Geometry""; ""3.1 Introduction"" ""3.2 Review of Principal Fiber Bundles""""3.2.1 Fiber Bundles""; ""3.2.2 Pull-Backs""; ""3.2.3 Principal Fiber Bundles""; ""3.2.4 Functoriality and Classification""; ""3.3 Basic Ideas of Non-commutative Geometry""; ""3.3.1 Two Classical Dualities Between Spaces and Algebras""; ""3.3.2 Non-commutative Algebras""; ""3.3.3 Extending Basic Operations to Non-commutative Spaces""; ""3.4 From Groups to Hopf Algebras""; ""3.4.1 Algebraic Groups""; ""3.4.2 Bialgebras""; ""3.4.3 Hopf Algebras""; ""3.4.4 Examples of Hopf Algebras from Finite Groups""; ""3.4.5 The Heyneman -- Sweedler Sigma Notation"" ""3.5 Quantum Groups Associated with SL2(mathbbC)""""3.5.1 The Quantum Coordinate Algebra of SL2(mathbbC)""; ""3.5.2 A Quotient of SLq(2)""; ""3.5.3 The Quantum Enveloping Algebra of mathfraksl(2)""; ""3.5.4 A Finite-Dimensional Quotient of Uq mathfraksl(2)""; ""3.6 Group Actions in Non-commutative Geometry""; ""3.6.1 Comodule-Algebras""; ""3.6.2 Group-Graded Algebras""; ""3.6.3 Algebras with Group Actions""; ""3.6.4 The Quantum Plane and Its SLq(2)-coaction""; ""3.6.5 Quantum Homogeneous Spaces""; ""3.7 Hopf Galois Extensions""; ""3.7.1 Definition and Examples""
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Copyright Date: 2017
• Extent: 1 online resource (x, 341 pages), illustrations
• Subjects: 530.14/3; Physics; Geometric quantization; Noncommutative differential geometry; Geometry, Algebraic; Mathematical physics; Quantum field theory; SCIENCE -- Energy; SCIENCE -- Mechanics -- General; SCIENCE -- Physics -- General; Geometric quantization; Geometry, Algebraic; Mathematical physics; Noncommutative differential geometry; Quantum field theory; Physics; Quantum Field Theories, String Theory; Mathematical Physics; Algebraic Geometry; Science -- Mathematical Physics; Mathematics -- Geometry -- Algebraic; Mathematical physics; Algebraic geometry; Science -- Quantum Theory; Statistical physics; Electronic books
• Languages: English
• ISBNs: 9783319654270; 3319654276; 3319654268; 9783319654263
• Related ISBNs: 9783319654263
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed November 02, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.