Mathematical Topics Between Classical and Quantum Mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1998
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "algebraic" and "geometric" with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper ator algebras, and their state spaces, which is based on this relationship |
| Beschreibung: | 1 Online-Ressource (XIX, 529 p) |
| ISBN: | 9781461216803 9781461272427 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-1-4612-1680-3 |
Internformat
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| 245 | 1 | 0 | |a Mathematical Topics Between Classical and Quantum Mechanics |c by N. P. Landsman |
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| 500 | |a Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "algebraic" and "geometric" with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper ator algebras, and their state spaces, which is based on this relationship | ||
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Datensatz im Suchindex
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1680-3 |
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| id | DE-604.BV042419885 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461216803 9781461272427 |
| issn | 1439-7382 |
| language | English |
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| spelling | Landsman, N. P. 1963- Verfasser (DE-588)172216699 aut Mathematical Topics Between Classical and Quantum Mechanics by N. P. Landsman New York, NY Springer New York 1998 1 Online-Ressource (XIX, 529 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "algebraic" and "geometric" with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper ator algebras, and their state spaces, which is based on this relationship Physics Theoretical, Mathematical and Computational Physics Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Mechanik (DE-588)4038168-7 s Mathematische Physik (DE-588)4037952-8 s DE-604 https://doi.org/10.1007/978-1-4612-1680-3 Verlag Volltext |
| spellingShingle | Landsman, N. P. 1963- Mathematical Topics Between Classical and Quantum Mechanics Physics Theoretical, Mathematical and Computational Physics Quantenmechanik (DE-588)4047989-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4037952-8 (DE-588)4038168-7 |
| title | Mathematical Topics Between Classical and Quantum Mechanics |
| title_auth | Mathematical Topics Between Classical and Quantum Mechanics |
| title_exact_search | Mathematical Topics Between Classical and Quantum Mechanics |
| title_full | Mathematical Topics Between Classical and Quantum Mechanics by N. P. Landsman |
| title_fullStr | Mathematical Topics Between Classical and Quantum Mechanics by N. P. Landsman |
| title_full_unstemmed | Mathematical Topics Between Classical and Quantum Mechanics by N. P. Landsman |
| title_short | Mathematical Topics Between Classical and Quantum Mechanics |
| title_sort | mathematical topics between classical and quantum mechanics |
| topic | Physics Theoretical, Mathematical and Computational Physics Quantenmechanik (DE-588)4047989-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics Quantenmechanik Mathematische Physik Mechanik |
| url | https://doi.org/10.1007/978-1-4612-1680-3 |
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