# Foundations of Quantum Theory

## From Classical Concepts to Operator Algebras

Part of the Fundamental Theories of Physics book series (FTPH, volume 188)

Open Access

Book
Part of the Fundamental Theories of Physics book series (FTPH, volume 188)

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.

This book is Open Access under a CC BY licence.

Quantum measurement problem Spontaneous symmetry breaking Open Access von Neumann operator algebras C*-algebras Quantum mechanics and topos theory Formalized Copenhagen Interpretation Born rule Bohrification

- DOI https://doi.org/10.1007/978-3-319-51777-3
- Copyright Information The Author(s) 2017
- Publisher Name Springer, Cham
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-319-51776-6
- Online ISBN 978-3-319-51777-3
- Series Print ISSN 0168-1222
- Series Online ISSN 2365-6425
- About this book