Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation by Valter Moretti
In this second English edition (third, if one includes the first Italian one), a large number of typos and errors of various kinds have been amended. The author has added more than 100 pages of fresh material, both mathematical and physical, in particular regarding the notion of super election rules—addressed from several different angles—the machinery of von Neumann algebras and the abstract algebraic formulation. I have considerably expanded the lattice approach to Quantum Mechanics in Chap. 7, which now contains precise statements leading up to Solèr’s theorem on the characterization of quantum lattices, as well as generalized versions of Gleason’s theorem. As a matter of fact, Chap. 7 and the related Chap. 11 have been completely reorganized.
Author has incorporated a variety of results on the theory of von Neumann algebras and a broader discussion on the mathematical formulation of super selection rules, also in relation to the von Neumann algebra of observables. The corresponding preparatory material has been fitted into Chap. 3. Chapter 12 has been developed further, in order to include technical facts concerning groups of quantum symmetries and their strongly continuous unitary representations. I have examined in detail the relationship between Nelson domains and Gårding domains. Each chapter has been enriched by many new exercises, remarks, examples and references.
Content of Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation by Valter Moretti book
- Introduction and Mathematical Backgrounds
- Normed and Banach Spaces, Examples and Applications
- Hilbert Spaces and Bounded Operators
- Families of Compact Operators on Hilbert Spaces and Fundamental Properties
- Densely-Defined Unbounded Operators on Hilbert Spaces
- Phenomenology of Quantum Systems and Wave Mechanics: An Overview
- The First 4 Axioms of QM: Propositions, Quantum States and Observables
- Spectral Theory I: Generalities, Abstract C∗ -Algebras and Operators in B(H)
- Spectral Theory II: Unbounded Operators on Hilbert Spaces
- Spectral Theory III: Applications
- Mathematical Formulation of Non-relativistic Quantum Mechanics
- Introduction to Quantum Symmetries
- Selected Advanced Topics in Quantum Mechanics
- Introduction to the Algebraic Formulation of Quantum Theories
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