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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 343 (17 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
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 20 (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
Double Fell bundles over discrete double groupoids with folding
, 2008
"... In this paper we construct the notions of double Fell bundle and double C*category for possible future use as tools to describe noncommutative spaces, in particular in finite dimensions. We identify the algebra of sections of a double Fell line bundle over a discrete double groupoid with folding wit ..."
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Cited by 1 (0 self)
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with the convolution algebra of the latter. This turns out to be what one might call a double C*algebra. We generalise the GelfandNaimarkSegal construction to double C*categories and we form the dual category for a saturated double Fell bundle using the TomitaTakesaki involution.
hepth/9603053 Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... Abstract. 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 ..."
Abstract
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−1 where D 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