Download this **PDF **book: Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation (UNITEXT, 110) 2nd ed. 2017 Edition by Valter Moretti

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."

## 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.

## Contents:

1 Introduction and Mathematical Backgrounds

2 Normed and Banach Spaces, Examples and Applications

3 Hilbert Spaces and Bounded Operators

4 Families of Compact Operators on Hilbert Spaces and Fundamental Properties

5 Densely-Defined Unbounded Operators on Hilbert Spaces

6 Phenomenology of Quantum Systems and Wave Mechanics: An Overview

7 The First 4 Axioms of QM: Propositions, Quantum States and Observables

8 Spectral Theory I: Generalities, Abstract C-Algebras and Operators in BÃ°HÃž

9 Spectral Theory II: Unbounded Operators on Hilbert Spaces

10 Spectral Theory III: Applications

11 Mathematical Formulation of Non-relativistic Quantum Mechanics

12 Introduction to Quantum Symmetries

13 Selected Advanced Topics in Quantum Mechanics

14 Introduction to the Algebraic Formulation of Quantum Theories

## About the book:

Publisher : Springer; 2nd ed. 2017 edition (February 14, 2018)

Language : English

Pages : 972

File : **PDF**, 10MB

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