Frontiers In Number Theory Physics And Geometry Ii

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Frontiers In Number Theory Physics And Geometry Ii

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Author : Pierre E. Cartier
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-18

Frontiers In Number Theory Physics And Geometry Ii written by Pierre E. Cartier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Mathematics categories.

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

Frontiers In Number Theory Physics And Geometry I

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Author : Pierre Cartier
language : en
Publisher:
Release Date : 2006

Frontiers In Number Theory Physics And Geometry I written by Pierre Cartier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This text (together with a forthcoming second volume) presents most of the courses and seminars delivered at the meeting entitled "Frontiers in number theory, physics and geometry" which took place at the Centre de Physique des Houches in the French Alps, March 9-12, 2003.

Foundations Of Mathematics And Physics One Century After Hilbert

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Author : Joseph Kouneiher
language : en
Publisher: Springer
Release Date : 2018-05-26

Foundations Of Mathematics And Physics One Century After Hilbert written by Joseph Kouneiher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-26 with Science categories.

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Basic Noncommutative Geometry

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Author : Masoud Khalkhali
language : en
Publisher: European Mathematical Society
Release Date : 2009

Basic Noncommutative Geometry written by Masoud Khalkhali and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.

Discrete Mechanics Geometric Integration And Lie Butcher Series

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Author : Kurusch Ebrahimi-Fard
language : en
Publisher: Springer
Release Date : 2018-11-05

Discrete Mechanics Geometric Integration And Lie Butcher Series written by Kurusch Ebrahimi-Fard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.

This volume resulted from presentations given at the international “Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie–Butcher Series”, that took place at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.

Renormalization And Galois Theories

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Author : Frédéric Fauvet
language : en
Publisher: European Mathematical Society
Release Date : 2009

Renormalization And Galois Theories written by Frédéric Fauvet and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.

Feynman S Operational Calculus And Beyond

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Author : Gerald W. Johnson
language : en
Publisher: Oxford Mathematical Monographs
Release Date : 2015

Feynman S Operational Calculus And Beyond written by Gerald W. Johnson and has been published by Oxford Mathematical Monographs this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Biography & Autobiography categories.

This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.

Integrability From Statistical Systems To Gauge Theory

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Author : Patrick Dorey
language : en
Publisher:
Release Date : 2019

Integrability From Statistical Systems To Gauge Theory written by Patrick Dorey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.

This volume contains lectures delivered at the Les Houches Summer School 'Integrability: from statistical systems to gauge theory' held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View

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Author : Gabriella Böhm
language : en
Publisher: Springer
Release Date : 2018-11-01

Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View written by Gabriella Böhm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-01 with Mathematics categories.

These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.

Feynman Amplitudes Periods And Motives

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Author : Luis Álvarez-Cónsul
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-24

Feynman Amplitudes Periods And Motives written by Luis Álvarez-Cónsul and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.

This volume contains the proceedings of the International Research Workshop on Periods and Motives--A Modern Perspective on Renormalization, held from July 2-6, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral. Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged. The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics.