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17
Roiban,Renormalization of Quantum Field Theories on Noncommutative R d , II.YangMills
"... Abstract: A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus g 2surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes of diagrams in the scalar field theories. We propose ..."
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Cited by 86 (1 self)
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Abstract: A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus g 2surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes of diagrams in the scalar field theories. We propose a noncommutative analog of BogoliubovParasiuk’s recursive subtraction formula and show that the subtracted graphs from a class Ωd satisfy the conditions of the convergence theorem. For a generic scalar noncommutative quantum field theory on R d, the class Ωd is smaller than the class of all diagrams in the theory. This leaves open the question of perturbative renormalizability of noncommutative field theories. We comment on how the supersymmetry can improve the situation and suggest that a noncommutative
Lectures on graded differential algebras and noncommutative geometry
, 1999
"... These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments. ..."
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Cited by 22 (3 self)
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These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
Lectures On Alain Connes' Non Commutative Geometry And Applications To Fundamental Interactions
, 1994
"... We introduce the reader to Alain Connes non commutative differential geometry, and sketch the applications made to date to (the lagrangian level of) fundamental physical interactions. ..."
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Cited by 5 (1 self)
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We introduce the reader to Alain Connes non commutative differential geometry, and sketch the applications made to date to (the lagrangian level of) fundamental physical interactions.
The Standard Model
 in Noncommutative Geometry and Fermion Doubling, Phys. Lett. B416
, 1998
"... Massive neutrinos can be accommodated into the noncommutative geometry reinterpretation ..."
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Cited by 5 (0 self)
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Massive neutrinos can be accommodated into the noncommutative geometry reinterpretation
Noncommutative Geometry for Pedestrians
"... A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of spacetime and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to ..."
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Cited by 3 (0 self)
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A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of spacetime and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature.
Inner fluctuations of the . . .
, 2006
"... We prove in the general framework of noncommutative geometry that the inner fluctuations of the spectral action can be computed as residues and give exactly the counterterms for the Feynman graphs with fermionic internal lines. We show that for geometries of dimension less or equal to four the obt ..."
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We prove in the general framework of noncommutative geometry that the inner fluctuations of the spectral action can be computed as residues and give exactly the counterterms for the Feynman graphs with fermionic internal lines. We show that for geometries of dimension less or equal to four the obtained terms add up to a sum of a YangMills action with a ChernSimons action.
of the Graduiertenkolleg ‘Physical Systems with Many Degrees of Freedom’ Universität Heidelberg
, 2002
"... We try to give a pedagogical introduction to Connes ’ derivation of the standard model of electromagnetic, weak and strong forces from gravity. Lectures given at the Autumn School “Topology and Geometry in Physics” ..."
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We try to give a pedagogical introduction to Connes ’ derivation of the standard model of electromagnetic, weak and strong forces from gravity. Lectures given at the Autumn School “Topology and Geometry in Physics”
and Université de Provence
, 2007
"... We try to give a pedagogical introduction to Connes ’ derivation of the standard model of electromagnetic, weak and strong forces from gravity. Lectures given at the Autumn School “Topology and Geometry in Physics” ..."
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We try to give a pedagogical introduction to Connes ’ derivation of the standard model of electromagnetic, weak and strong forces from gravity. Lectures given at the Autumn School “Topology and Geometry in Physics”
ITPSB9961 Renormalization of Quantum Field Theories on
, 1999
"... A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus g 2surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes of diagrams in the scalar field theories. We propose a noncomm ..."
Abstract
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A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus g 2surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes of diagrams in the scalar field theories. We propose a noncommutative analog of BogoliubovParasiuk’s recursive subtraction formula and show that the subtracted graphs from a class Ωd satisfy the conditions of the convergence theorem. For any scalar noncommutative quantum field theory on R d, the class Ωd is smaller than the class of all diagrams in the scalar NQFT, implying that the noncommutative scalar field theories cannot be renormalized. We discuss how the supersymmetry can improve the situation and argue that a noncommutative analog of WessZumino model is renormalizable.