Overview
- Most chapters are accompanied by exercises, many of which are solved explicitly
- Presents several examples of the physical formalism
- Can be used as an advanced introductory text on spectral theory and operator algebras
Part of the book series: UNITEXT (UNITEXT, volume 110)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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About this book
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory.
Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories.
Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."
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Table of contents (14 chapters)
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Authors and Affiliations
About the author
Prof. Valter Moretti is a Full Professor of Mathematical Physics at the University of Trento (Italy). His research interests include rigorous quantum field theory in curved spacetime, mathematical aspects of quantum mechanics and general relativity, the applications of operator algebras, functional analysis and global analysis to quantum field theory, and mathematical (analytic and geometric) methods for physics.
Bibliographic Information
Book Title: Spectral Theory and Quantum Mechanics
Book Subtitle: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation
Authors: Valter Moretti
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-319-70706-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-70705-1Published: 14 February 2018
eBook ISBN: 978-3-319-70706-8Published: 30 January 2018
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 2
Number of Pages: XXII, 950
Topics: Applications of Mathematics, Mathematical Methods in Physics, Analysis