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Author | Title | Accn# | Year | Item Type | Claims |
| 1 |
Cardona, Alexander |
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics |
I09980 |
2017 |
eBook |
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| 2 |
Ocampo, Hernan |
Geometric and Topological Methods for Quantum Field Theory |
I07121 |
2005 |
eBook |
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1.
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| Title | Quantization, Geometry and Noncommutative Structures in Mathematics and Physics |
| Author(s) | Cardona, Alexander;Morales, Pedro;Ocampo, Hern??n;Paycha, Sylvie;Reyes Lega, Andr??s F |
| Publication | Cham, Springer International Publishing, 2017. |
| Description | X, 341 p. 6 illus : online resource |
| Abstract Note | 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 non-commutative 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 Nicol??s Andruskiewitsch. ?? The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, 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 non-commutativity. 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 Batalin-Vilkovisky 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 |
| ISBN,Price | 9783319654270 |
| Keyword(s) | 1. ALGEBRAIC GEOMETRY
2. EBOOK
3. EBOOK - SPRINGER
4. MATHEMATICAL PHYSICS
5. Quantum Field Theories, String Theory
6. QUANTUM FIELD THEORY
7. STRING THEORY
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| Item Type | eBook |
Multi-Media Links
Please Click here for eBook
Circulation Data
| Accession# | |
Call# | Status | Issued To | Return Due On | Physical Location |
| I09980 |
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On Shelf |
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2.
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| Title | Geometric and Topological Methods for Quantum Field Theory |
| Author(s) | Ocampo, Hernan;Paycha, Sylvie;Vargas, Andr??s |
| Publication | Berlin, Heidelberg, Springer Berlin Heidelberg, 2005. |
| Description | XV, 230 p : online resource |
| Abstract Note | This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently |
| ISBN,Price | 9783540315223 |
| Keyword(s) | 1. COMPLEX MANIFOLDS
2. DIFFERENTIAL GEOMETRY
3. EBOOK
4. EBOOK - SPRINGER
5. Elementary particles (Physics)
6. Elementary Particles, Quantum Field Theory
7. Manifolds (Mathematics)
8. Manifolds and Cell Complexes (incl. Diff.Topology)
9. Mathematical Methods in Physics
10. PHYSICS
11. Quantum Field Theories, String Theory
12. QUANTUM FIELD THEORY
13. STRING THEORY
|
| Item Type | eBook |
Multi-Media Links
Please Click here for eBook
Circulation Data
| Accession# | |
Call# | Status | Issued To | Return Due On | Physical Location |
| I07121 |
|
|
On Shelf |
|
|
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