Lectures on the Mathematics of Quantum Mechanics I
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered....
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| Language: | English |
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Paris :
Atlantis Press : Imprint: Atlantis Press,
2015.
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| Edition: | 1st ed. 2015. |
| Series: | Atlantis Studies in Mathematical Physics: Theory and Applications,
1 |
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| Online Access: | https://doi.org/10.2991/978-94-6239-118-5 |
Table of Contents:
- Elements of the history of Quantum Mechanics I
- Elements of the history of Quantum Mechanics II
- Axioms, states, observables, measurement, difficulties
- Entanglement, decoherence, Bell’s inequalities, alternative theories
- Automorphisms; Quantum dynamics; Theorems of Wigner, Kadison, Segal; Continuity and generators
- Operators on Hilbert spaces I; Basic elements
- Quadratic forms
- Properties of free motion, Anholonomy, Geometric phase
- Elements of C ∗-algebras, GNS representation, automorphisms and dynamical systems
- Derivations and generators. K.M.S. condition. Elements of modular structure. Standard form
- Semigroups and dissipations. Markov approximation
- Quantum dynamical semigroups I
- Positivity preserving contraction semigroups on C ∗-algebras
- Conditional expectations
- Complete Dissipations
- Weyl system, Weyl algebra, lifting symplectic maps
- Magnetic Weyl algebra
- A Theorem of Segal
- Representations of Bargmann, Segal, Fock
- Second quantization
- Other quantizations (deformation, geometric).