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[Free Download.vApV] Feynman Motives

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Book Details :
Published on: 2009-12-30
Released on: 2009-12-30
Original language: English

This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer. Two different approaches to the subject are described. The first, a “bottom-up” approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of Bloch–Esnault–Kreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, “top-down” approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann–Hilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and n The nature of anecdotes SkepticReport What is an anecdote? Why do we pay special attention to some experiences and tell about them? Are they true or false? Can they be trusted? Why do we selectively ... Skepticism - RationalWiki Skepticism (or scepticism) is the art of constantly questioning and doubting claims and assertions and holding that the accumulation of evidence is of ... Mathematics -- J.S. Milne Books Etale Cohomology. Hodge Cycles Motives and Shimura Varieties Arithmetic Duality Theorems Automorphic Forms Shimura Varieties and L-functions ... A neuroscientist explains why artificially intelligent ... A failure to recognize the importance of this strong/weak distinction could be contributing to Hawking and Musks existential worries both of whom believe that we ... Nanotechnology - Zyvex Nanotechnology is an expected future manufacturing technology that will make most products lighter stronger cleaner less expensive and more precise. Noncommutative Geometry Quantum Fields and Motives Alain ... Noncommutative Geometry Quantum Fields and Motives Alain Connes Matilde Marcolli A. Connes: College de France 3 rue dUlm Paris F-75005 France Alain Connes -- Downloads The official website of Alain Connes. ... Noncommutative geometry and reality 2.5 MB; Hecke algebras type III factors and phase transitions with spontaneous symmetry ... The Word "Hacker" - Paul Graham April 2004 To the popular press "hacker" means someone who breaks into computers. Among programmers it means a good programmer. But the two meanings are connected. Trump Nation - The Atlantic Our latest commentary from readers and James Fallows on the ramifications of Donald Trumps rise. Hakkasan Group Hakkasan Group is an international company owning and operating several of the worlds most acclaimed fine-dining and lifestyle brands.
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