Introduction - Alain Connes
NONCOMMUTATIVE GEOMETRY AND PHYSICS 6 where T is the pole part in dimensional regularization. Finally the renormalized value of the graph ¡ is given by R(¡) = R(¡)+ C(¡) = U(¡)+ C(¡)+ X °‰¡ C(°)U(¡=°) While this procedure is perfectly justifled from the physics standpoint it took a long
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Noncommutative Geometry Alain Connes
www.alainconnes.orgCONTENTS 5 Appendix A. Crossed Products of von Neumann Algebras 537 Appendix B. Correspondences 539 Chapter 6. The metric aspect of noncommutative geometry 552
The Longitudinal Index Theorem for Foliations
www.alainconnes.orgof an immersion, one gets that in all cases the map K(X) →K(Y) given by f! coincides with the classical wrong way map in K-theory. This statement is …
arXiv:hep-th/0605011 v3 20 Jun 2006 - Alain Connes
www.alainconnes.orgarXiv:hep-th/0605011 v3 20 Jun 2006 INNER FLUCTUATIONS OF THE SPECTRAL ACTION ALAIN CONNES AND ALI H. CHAMSEDDINE Abstract. We prove in the general framework of noncommutative geometry that the inner fluc-
Hopf Algebras, Renormalization and …
www.alainconnes.orgarXiv:hep-th/9808042 v1 7 Aug 1998 Hopf Algebras, Renormalization and Noncommutative Geometry Alain CONNES IHES Dirk KREIMER Mainz Univ. August 1998, IHES/M/98/60
A VIEW OF MATHEMATICS Alain CONNES
www.alainconnes.orgA VIEW OF MATHEMATICS Alain CONNES Mathematics is the backbone of modern science and a remarkably e cient source of new concepts and tools to understand the \reality" in which we participate.
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