| Edition |
1st ed. |
| Description |
1 online resource (xi, 407 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematics studies ; 186 |
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North-Holland mathematics studies ; 186.
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| Summary |
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in <IT>N</IT> = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory. |
| Bibliography |
Includes bibliographical references and index. |
| Note |
Print version record. |
| Contents |
Front Cover; Quantum Theory, Deformation and Integrability; Copyright Page; Contents; Preface; CHAPTER 1. QUANTIZATION AND INTEGRABILITY; CHAPTER 2. GEOMETRY AND EMBEDDING; CHAPTER 3. CLASSICAL AND QUANTUM INTEGRABILITY; CHAPTER 4. DISCRETE GEOMETRY AND MOYAL; CHAPTER 5. WHITHAM THEORY; CHAPTER 6. GEOMETRY AND DEFORMATION QUANTIZATION; Bibliography; Index. |
| Subject |
Geometric quantization.
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Operator algebras.
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Mathematical physics.
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Quantification géométrique.
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Algèbres d'opérateurs.
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Physique mathématique.
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SCIENCE -- Physics -- Quantum Theory.
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Geometric quantization
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Mathematical physics
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Operator algebras
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| Other Form: |
Print version: Carroll, Robert Wayne, 1930- Quantum theory, deformation, and integrability. 1st ed. New York : Elsevier Science B.V., 2000 0444506217 9780444506214 (DLC) 00047685 (OCoLC)45024489 |
| ISBN |
9780444506214 |
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0444506217 |
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9780080540085 (electronic bk.) |
|
0080540082 (electronic bk.) |
| Standard No. |
AU@ 000048129390 |
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CHNEW 001006562 |
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DEBBG BV036962322 |
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DEBBG BV039830190 |
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DEBBG BV042317329 |
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DEBSZ 276792254 |
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DEBSZ 482355123 |
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NZ1 12433527 |
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NZ1 15192881 |
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DKDLA 820120-katalog:9910110076805765 |
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