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Geometric, Algebraic and Topological Methods for Quantum Field Theory
Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.
Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2011 Villa De Leyva Summer School
Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.
International Conference on Theoretical Physics
The International Conference on Theoretical Physics, TH-2002, took place in Paris from July 22 to 27 in the Conference Center of the UNESCO, the United Nations Educational Scientific and Cultural Organization, under aegis of the IUPAP, the International Union of Pure and Applied Physics and of the French and Euro pean Physical Societies, with a large support of several French, European and international Institutions. International and crossdisciplinary, TH-2002 welcomed around 1200 partic ipants representing all domains of modern theoretical physics. The conference offered a high-level scientific program, including 18 plenary lectures, 45 general lectures in thematic sessions and 140 more sp...
Noncommutative Cosmology
Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology.Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity.
Supersymmetric World, The: The Beginnings Of The Theory (Second Edition)
The story of the discovery of supersymmetry is a fascinating one, unlike that of any other major de-velopment in the history of science. This engaging book presents a view of the process, mainly in the words of people who participated. It combines anecdotal descriptions and personal reminiscences with more technical accounts of the trailblazers, covering the birth of the theory and its first years — the origin of the idea, four-dimensional field theory realization, and supergravity. The eyewit-nesses convey to us the drama of one of the deepest discoveries in theoretical physics in the 20th century. This book will be equally interesting and useful to young researchers in high energy physic...
Lumen Naturae
Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in...
In the Shadow of Sectarianism
Contrary to the conventional wisdom that sectarianism is intrinsically linked to violence, bloodshed, or social disharmony, Max Weiss uncovers the complex roots of Shiʿi sectarianism in twentieth-century Lebanon. The template for conflicted relations between the Lebanese state and Shiʿi society arose under French Mandate rule through a process of gradual transformation, long before the political mobilization of the Shiʿi community under the charismatic Imam Musa al-Sadr and his Movement of the Deprived, and decades before the radicalization linked to Hizballah. Throughout the period, the Shiʿi community was buffeted by crosscutting political, religious, and ideological currents: transnational affiliations versus local concerns; the competing pull of Arab nationalism and Lebanese nationalism; loyalty to Jabal ʿAmil, the cultural heartland of Shiʿi Lebanon; and the modernization of religious and juridical traditions. Uncoupling the beginnings of modern Shiʿi collective identity from the rise of political Shiʿism, Weiss transforms our understanding of the nature of sectarianism and shows why in Lebanon it has been both so productive and so destructive at the same time.
Noncommutative Geometry, Quantum Fields and Motives
This book carries the unifying theme of the interaction among noncommutative geometry, theoretical physics and number theory. The detailed text, co-authored by Fields Medal winner Alain Connes, stresses the relevance of noncommutative geometry in dealing with two spaces: space-time and the space of prime numbers. The book includes significantly more detail than other monographs covering similar topics.
Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions
Contents include: Hochschild Homology of Function Algebras Associated with Singularities; On the KK-Theory of Stable Projective Limits; Noncommutative Integrability; Gauge Invariance of the Chern-Simons Action in Noncommutative Geometry; The Analysis of the Hochshild Homology; Coproducts and Operations on Cyclic Cohomology; Powers of Quantum Matrices and Relations Between Them; Introductory Notes on Extensions of Hopf Algebras; Hopf Algebras from the Quantum Geometry Point of View; Equation Pentagonale, Bige bres et Espaces de Modules; Chiral Anomalies in the Spectral Action; Standard Model and Unimodularity Condition; On Feynman Graphs as Elements of a Hopf Algebra.
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