Equivariant Cohomology and Localization of Path Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Equivariant Cohomology and Localization of Path Integrals write by Richard J. Szabo. This book was released on 2003-07-01. Equivariant Cohomology and Localization of Path Integrals available in PDF, EPUB and Kindle. 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.
Introductory Lectures on Equivariant Cohomology
Introductory Lectures on Equivariant Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introductory Lectures on Equivariant Cohomology write by Loring W. Tu. This book was released on 2020-03-03. Introductory Lectures on Equivariant Cohomology available in PDF, EPUB and Kindle. This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
Functional Integration
Functional Integration - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functional Integration write by Cécile Dewitt-Morette. This book was released on 2013-11-11. Functional Integration available in PDF, EPUB and Kindle. 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.
Particles and Fields
Particles and Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Particles and Fields write by Gordon W. Semenoff. This book was released on 2012-12-06. Particles and Fields available in PDF, EPUB and Kindle. 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).
Stochastic Analysis: Classical And Quantum: Perspectives Of White Noise Theory
Stochastic Analysis: Classical And Quantum: Perspectives Of White Noise Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Analysis: Classical And Quantum: Perspectives Of White Noise Theory write by Takeyuki Hida. This book was released on 2005-10-06. Stochastic Analysis: Classical And Quantum: Perspectives Of White Noise Theory available in PDF, EPUB and Kindle. This volume includes papers by leading mathematicians in the fields of stochastic analysis, white noise theory and quantum information, together with their applications. The papers selected were presented at the International Conference on Stochastic Analysis: Classical and Quantum held at Meijo University, Nagoya, Japan from 1 to 5 November 2004. The large range of subjects covers the latest research in probability theory.
