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598
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 354 (18 self)
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is the Dirac operator. We extend these simple relations to the non commutative case using Tomita’s involution J. We then write a spectral action, the trace of a function of the length element in Planck units, which when applied to the non commutative geometry of the Standard Model will be shown (in a joint
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
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Cited by 397 (26 self)
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A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
TomitaTakesaki Modular Theory
"... We provide an brief overview of Tomita–Takesaki modular theory and some of its applications to mathematical physics. This is an article commissioned by the Encyclopedia of Mathematical Physics, edited by J.P. Francoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house. 1 Bas ..."
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Cited by 23 (0 self)
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We provide an brief overview of Tomita–Takesaki modular theory and some of its applications to mathematical physics. This is an article commissioned by the Encyclopedia of Mathematical Physics, edited by J.P. Francoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house. 1
Boundary conformal fields and Tomita–Takesaki theory
, 2003
"... Motivated by formal similarities between the continuum limit of the Ising model and the Unruh effect, this paper connects the notion of an Ishibashi state in boundary conformal field theory with the Tomita–Takesaki theory for operator algebras. A geometrical approach to the definition of Ishibashi s ..."
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Motivated by formal similarities between the continuum limit of the Ising model and the Unruh effect, this paper connects the notion of an Ishibashi state in boundary conformal field theory with the Tomita–Takesaki theory for operator algebras. A geometrical approach to the definition of Ishibashi
Saitô– Tomita–Lusin theorem for JB*triple and applications
 Q. J. Math. Oxford
, 2006
"... A theorem of Lusin is proved in the nonordered context of JB ∗triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed unit ballls of JB ∗triples and duals. 1. Introduction and ..."
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Cited by 7 (5 self)
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A theorem of Lusin is proved in the nonordered context of JB ∗triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed unit ballls of JB ∗triples and duals. 1. Introduction and
Application of TomitaTakesaki theory in algebraic euclidean field theories
, 2008
"... The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one should be able to extract information about the behavior of the ..."
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covariant quantum field theory model in the sense of R. Haag and D. Kastler. Within the framework of R. Haag and D. Kastler, the physical concept of PCT symmetry and spin and statistics is related to the TomitaTakesaki theory of von Neumann algebras and this important aspects has been studied by several
Physics © by SpringerVerlag 1976 Classical KMS Condition and TomitaTakesaki Theory
"... Abstract. Relationships between the classical KMS condition and the time evolution for classical systems are discussed. 1. ..."
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Abstract. Relationships between the classical KMS condition and the time evolution for classical systems are discussed. 1.
Von Neumann Algebras
, 2009
"... The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. In this sense it is opposite in spirit from the treatises of ..."
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Cited by 111 (5 self)
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The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. In this sense it is opposite in spirit from the treatises of
Results 1  10
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598