Equivariant Cohomology And Localization Of Path Integrals

Author : Richard J. Szabo
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 50,9 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540465508

Get Book

Equivariant Cohomology and Localization of Path Integrals by Richard J. Szabo Pdf

This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.

Author : Olav Tirkkonen
Publisher : Unknown
Page : 100 pages
File Size : 42,9 Mb
Release : 1994
Category : Localization theory
ISBN : 9514567633

Get Book

Equivariant Localization of Path Integrals by Olav Tirkkonen Pdf

Author : Cécile Dewitt-Morette,Antoine Folacci
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 55,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489903198

Get Book

Functional Integration by Cécile Dewitt-Morette,Antoine Folacci Pdf

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

Author : Gordon W. Semenoff,Luc Vinet
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461214106

Get Book

Particles and Fields by Gordon W. Semenoff,Luc Vinet Pdf

The focus of this volume is on quantum field theory: inegrable theories, statistical systems, and applications to condensed-matter physics. It covers some of the most significant recent advances in theoretical physics at a level accessible to advanced graduate students. The contributions, each by a noted researcher, dicuss such topics as: some remarkable features of integrable Toda field theories (E. Corrigan), properties of a gas of interacting Fermions in a lattice of magnetic ions (J. Feldman &. al.), how quantum groups arise in three-dimensional topological quantum field thory (D. Freed), a method for computing correlation functions of solvable lattice models (T. Miwa), matrix models discussed from the point of view of integrable systems (A. Morozov), localization of path integrals in certain equivariant cohomologies (A. Niemi), Calogero-Moser systems (S. Ruijsenaars), planar gauge theories with broken symmetries (M. de Wild Propitius & F.A. Bais), quantum-Hall fluids (A. Capelli & al.), spectral theory of quantum vortex operators (P.I. Ettinghoff).

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814479172

Get Book

Stochastic Analysis: Classical and Quantum by Anonim Pdf

Author : Andrei A Bytsenko,Antonio E Goncalves,Bruto M Pimentel
Publisher : World Scientific
Page : 213 pages
File Size : 54,7 Mb
Release : 2001-02-05
Category : Science
ISBN : 9789814491877

Get Book

Geometrical Aspects Of Quantum Fields - Proceedings Of The 2000 Londrina Workshop by Andrei A Bytsenko,Antonio E Goncalves,Bruto M Pimentel Pdf

This volume presents the following topics: non-Abelian Toda models, brief remarks for physicists on equivariant cohomology and the Duistermaat-Heckman formula, Casimir effect, quantum groups and their application to nuclear physics, quantum field theory, quantum gravity and the theory of extended objects, and black hole physics and cosmology.

Author : Taro Kimura
Publisher : Springer Nature
Page : 297 pages
File Size : 41,5 Mb
Release : 2021-07-05
Category : Science
ISBN : 9783030761905

Get Book

Instanton Counting, Quantum Geometry and Algebra by Taro Kimura Pdf

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

Author : Gregory L. Naber
Publisher : Walter de Gruyter GmbH & Co KG
Page : 570 pages
File Size : 52,8 Mb
Release : 2021-09-20
Category : Science
ISBN : 9783110751949

Get Book

Quantum Mechanics by Gregory L. Naber Pdf

This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions. The author addresses all these topics with utter mathematical rigor. The high number of instructive Appendices and numerous Remark sections supply the necessary background knowledge.

Author : Leon Armenovich Takhtadzhi͡an
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 43,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846308

Get Book

Quantum Mechanics for Mathematicians by Leon Armenovich Takhtadzhi͡an Pdf

Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.

Author : Gunnar Carlsson,Mikael Vejdemo-Johansson
Publisher : Cambridge University Press
Page : 233 pages
File Size : 44,6 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781108838658

Get Book

Topological Data Analysis with Applications by Gunnar Carlsson,Mikael Vejdemo-Johansson Pdf

This timely text introduces topological data analysis from scratch, with detailed case studies.

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1060 pages
File Size : 51,7 Mb
Release : 2007-04-18
Category : Science
ISBN : 9783540347644

Get Book

Quantum Field Theory I: Basics in Mathematics and Physics by Eberhard Zeidler Pdf

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Author : Šárka Hošková-Mayerová,Cristina Flaut,Fabrizio Maturo
Publisher : Springer Nature
Page : 515 pages
File Size : 49,9 Mb
Release : 2021-01-13
Category : Technology & Engineering
ISBN : 9783030613341

Get Book

Algorithms as a Basis of Modern Applied Mathematics by Šárka Hošková-Mayerová,Cristina Flaut,Fabrizio Maturo Pdf

This book offers a self-contained guide to advanced algorithms and their applications in various fields of science. Gathering contributions by authoritative researchers in the field of mathematics, statistics and computer science, it aims at offering a comprehensive and up-to-date view of algorithms, including the theory behind them, as well as practical considerations, current limitations and solutions. It covers applications in energy management, decision making, computer networks, materials science, mechanics and process optimization. It offers an integrated and timely guide to important algorithms, and represents a valuable reference resource for graduate students and researchers in various fields of applied mathematics, statistics and engineering.

Author : Sonia Mazzucchi
Publisher : World Scientific
Page : 360 pages
File Size : 42,9 Mb
Release : 2021-11-16
Category : Science
ISBN : 9789811214806

Get Book

Mathematical Feynman Path Integrals And Their Applications (Second Edition) by Sonia Mazzucchi Pdf

Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.

Author : Jean-Pierre Françoise,Gregory L. Naber,Sheung Tsun Tsou
Publisher : Academic Press
Page : 736 pages
File Size : 46,9 Mb
Release : 2006
Category : Mathematics
ISBN : UCSC:32106018859873

Get Book

Encyclopedia of Mathematical Physics by Jean-Pierre Françoise,Gregory L. Naber,Sheung Tsun Tsou Pdf

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, France Gregory L. Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy.

Author : H. Gausterer,H. Grosse,L. Pittner
Publisher : Springer
Page : 408 pages
File Size : 50,8 Mb
Release : 2008-01-11
Category : Science
ISBN : 9783540465522

Get Book

Geometry and Quantum Physics by H. Gausterer,H. Grosse,L. Pittner Pdf

In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model.