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020 _a9783642357138
_9978-3-642-35713-8
024 7 _a10.1007/978-3-642-35713-8
_2doi
050 4 _aQC173.96-174.52
072 7 _aPHQ
_2bicssc
072 7 _aSCI057000
_2bisacsh
072 7 _aPHQ
_2thema
082 0 4 _a530.12
_223
100 1 _aFlori, Cecilia.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 2 _aA First Course in Topos Quantum Theory
_h[electronic resource] /
_cby Cecilia Flori.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXIII, 449 p. 8 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v868
505 0 _aIntroduction -- 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.
520 _aIn 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.
650 0 _aQuantum theory.
650 0 _aMathematical physics.
650 1 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642357145
776 0 8 _iPrinted edition:
_z9783642357121
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v868
856 4 0 _uhttps://doi.org/10.1007/978-3-642-35713-8
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c12292
_d12292