About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103642357121

ISBN-139783642357121

eBay Product ID (ePID)150634909

Product Key Features

Number of PagesXiii, 449 Pages

LanguageEnglish

Publication NameFirst Course in Topos Quantum Theory

SubjectGroup Theory, Physics / Quantum Theory, Physics / Mathematical & Computational

Publication Year2013

TypeTextbook

AuthorCecilia Flori

Subject AreaMathematics, Science

SeriesLecture Notes in Physics Ser.

FormatTrade Paperback

Dimensions

Item Height0.4 in

Item Weight245.6 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2013-933014

TitleLeadingA

Dewey Edition23

ReviewsFrom 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), From the reviews: "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)

Series Volume Number868

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal530.12

Table Of ContentIntroduction.- Philosophical Motivations.- Kochen-Specker Theorem.- Introducing Category Theory.- Functors.- The Category of Functors.- Topos.- Topos of Presheaves.- Topos Analogue of the State Space.- Topos Analogue of Propositions.- Topos Analogues of States.- Truth Values.- Quantity Value Object and Physical Quantities.- Sheaves.- Probabilities in Topos Quantum theory.- Group Action in Topos Quantum Theory.- Topos History Quantum Theory.- Normal Operators.- KMS States.- Future Research.- Topos and Logic.- Worked out Examples.

SynopsisIn 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., Introduction.- Philosophical Motivations.- Kochen-Specker Theorem.- Introducing Category Theory.- Functors.- The Category of Functors.- Topos.- Topos of Presheaves.- Topos Analogue of the State Space.- Topos Analogue of Propositions.- Topos Analogues of States.- Truth Values.- Quantity Value Object and Physical Quantities.- Sheaves.- Probabilities in Topos Quantum theory.- Group Action in Topos Quantum Theory.- Topos History Quantum Theory.- Normal Operators.- KMS States.- Future Research.- Topos and Logic.- Worked out Examples., 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., This book explains to graduate students and newcomers to the field how topos theory can be used to overcome critical issues in present-day quantum physics and how it brings quantum physics back to looking more like a neo-realist classical physics theory again.

LC Classification NumberQC173.96-174.52