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© 2013

A First Course in Topos Quantum Theory

  • Written by a leading researcher in the field

  • Concise course-tested textbook

  • Includes worked-out problems

Book

Part of the Lecture Notes in Physics book series (LNP, volume 868)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Cecilia Flori
    Pages 1-5
  3. Cecilia Flori
    Pages 7-12
  4. Cecilia Flori
    Pages 13-24
  5. Cecilia Flori
    Pages 25-61
  6. Cecilia Flori
    Pages 63-74
  7. Cecilia Flori
    Pages 75-84
  8. Cecilia Flori
    Pages 85-115
  9. Cecilia Flori
    Pages 117-129
  10. Cecilia Flori
    Pages 131-146
  11. Cecilia Flori
    Pages 147-162
  12. Cecilia Flori
    Pages 163-176
  13. Cecilia Flori
    Pages 177-190
  14. Cecilia Flori
    Pages 191-217
  15. Cecilia Flori
    Pages 219-247
  16. Cecilia Flori
    Pages 249-271
  17. Cecilia Flori
    Pages 273-306
  18. Cecilia Flori
    Pages 307-333
  19. Cecilia Flori
    Pages 335-350
  20. Cecilia Flori
    Pages 351-372

About this book

Introduction

In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity.

The present text adopts this point of view, addressing the following basic questions:  What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory?

A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory.

This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.

Keywords

Category Theory Foundations of Quantum Mechanics Kochen-Specker Theorem Quantum Logic Topos Quantum Theory Textbook Topos Theory

Authors and affiliations

  1. 1.Perimeter Inst. for Theor. StudiesWaterlooCanada

Bibliographic information

Reviews

From the reviews:

“This text presents a reformulation of quantum theory in terms of modern mathematical framework called topos theory. … This is one of the first text to address all of these aspects of topos quantum theory at the graduate student level.” (S. Moskaliuk, zbMATH, Vol. 1280, 2014)

“The book is self-contained and can be used as a textbook or self-study manual teaching the usage of category theory and topos theory in particular in theoretical physics or in investigating the foundations of quantum theory in mathematically rigorous terms. … the book is a very welcome contribution.” (Frank Antonsen, Mathematical Reviews, December, 2013)