Lecture Notes in Physics

A First Course in Topos Quantum Theory

Authors: Flori, Cecilia

  • Written by a leading researcher in the field
  • Concise course-tested textbook
  • Includes worked-out problems
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About this book

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.

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)

Table of contents (21 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-35713-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.95
price for USA
  • ISBN 978-3-642-35712-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A First Course in Topos Quantum Theory
Authors
Series Title
Lecture Notes in Physics
Series Volume
868
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-35713-8
DOI
10.1007/978-3-642-35713-8
Softcover ISBN
978-3-642-35712-1
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XIII, 449
Number of Illustrations and Tables
8 b/w illustrations
Topics