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La Matematica per il 3+2

Spectral Theory and Quantum Mechanics

Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation

Authors: Moretti, Valter

  • 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
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eBook 74,96 €
price for Italia (gross)
  • ISBN 978-3-319-70706-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 93,59 €
price for Italia (gross)
  • ISBN 978-3-319-70705-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 authors

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.

Table of contents (14 chapters)

  • Introduction and Mathematical Backgrounds

    Moretti, Valter

    Pages 1-38

    Preview Buy Chapter 30,44 €
  • Normed and Banach Spaces, Examples and Applications

    Moretti, Valter

    Pages 39-106

    Preview Buy Chapter 30,44 €
  • Hilbert Spaces and Bounded Operators

    Moretti, Valter

    Pages 107-196

    Preview Buy Chapter 30,44 €
  • Families of Compact Operators on Hilbert Spaces and Fundamental Properties

    Moretti, Valter

    Pages 197-249

    Preview Buy Chapter 30,44 €
  • Densely-Defined Unbounded Operators on Hilbert Spaces

    Moretti, Valter

    Pages 251-288

    Preview Buy Chapter 30,44 €

Buy this book

eBook 74,96 €
price for Italia (gross)
  • ISBN 978-3-319-70706-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 93,59 €
price for Italia (gross)
  • ISBN 978-3-319-70705-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Theory and Quantum Mechanics
Book Subtitle
Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation
Authors
Series Title
La Matematica per il 3+2
Series Volume
110
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-70706-8
DOI
10.1007/978-3-319-70706-8
Softcover ISBN
978-3-319-70705-1
Series ISSN
2038-5722
Edition Number
2
Number of Pages
XXII, 950
Topics