Joel Feldman, University of British Columbia, Vancouver, BC, Canada, and Horst Knorrer and Eugene Trubowitz, Eidgen Technische Hochschule, Zurich, Switzerland
Fermionic Functional Integrals and the Renormalization Group
Expected publication date is July 10, 2002
Description
This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory.
The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics.
This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and solutions.
Contents
Fermionic functional integrals
Fermionic expansions
Appendix A. Infinite-dimensional Grassman algebras
Appendix B. Pfaffians
Appendix C. Propagator bounds
Appendix D. Problem solutions
Bibliography
Details:
Series: CRM Monograph Series, Volume: 16
Publication Year: 2002
ISBN: 0-8218-2878-9
Paging: 115 pp.
Binding: Hardcover
Michael Barr, Peter Redpath Emeritus Professor of Pure Mathematics, McGill University, Montreal, QC, Canada
Acyclic Models
Expected publication date is July 14, 2002
Description
Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background.
It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology.
The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.
Contents
・Categories
・Abelian categories and homological algebra
・Chain complexes and simplicial objects
・Triples a la mode de Kan
・The main acyclic models theorem
・Cartan-Eilenberg Cohomology
・Other applications in algebra
・Applications in topology
・Bibliography
・Index
Details:
Series: CRM Monograph Series, Volume: 17
Publication Year: 2002
ISBN: 0-8218-2877-0
Paging: 179 pp.
Binding: Hardcover
Susumu Ariki, Research Institute for Mathematical Sciences, Kyoto University
Representations of Quantum Algebras
and Combinatorics of Young Tableaux
Expected publication date is July 11, 2002
Description
This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups.
Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras.
The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A_{r-1}^{(1)}$ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be the combinatorics of Young tableaux.
The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type.
The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, and related fields.
Contents
・Introduction
・The Serre relations
・Kac-Moody Lie algebras
・Crystal bases of $U_v$-modules
・The tensor product of crystals
・Crystal bases of $U_v^-$
・The canonical basis
・Existence and uniqueness (part I)
・Existence and uniqueness (part II)
・The Hayashi realization
・Description of the crystal graph of $V(\Lambda)$
・An overview of the application to Hecke algebras
・The Hecke algebra of type $G(m,1,n)$
・The proof of Theorem 12.5
・Reference guide
・Bibliography
・Index
Details:
Series: University Lecture Series, Volume: 26
Publication Year: 2002
ISBN: 0-8218-3232-8
Paging: 158 pp.
Binding: Softcover
Edited by: Raymond Chan, Chinese University of Hong Kong, Shatin, Hong Kong, China, Yue-Kuen Kwok, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China, David Yao, Columbia University, NY, NY, and Qiang Zhang, State University of New York at Stony Brook, NY
Applied Probability
Expected publication date is July 7, 2002
Description
This book presents articles on original material from invited talks given at the "IMS Workshop on Applied Probability" organized by the Institute of Mathematical Sciences at the Chinese University of Hong Kong in May 1999. The goal of the workshop was to promote research in applied probability for local mathematicians and engineers and to foster exchange with experts from other parts of the world. The main themes were mathematical finance and stochastic networks.
The topics range from the theoretical study, e.g., ergodic theory and diffusion processes, to very practical problems, such as convertible bonds with market risk and insider trading.
The wide scope of coverage in the book make it a helpful reference for graduate students and researchers, and for practitioners working in mathematical finance.
Titles in this series are copublished with International Press, Cambridge, MA.
Contents
・R. H. Chan and W. K. Ching -- A direct method for stochastic automata networks
・D. Chen -- Estimating the speed of random walks
・M.-F. Chen -- A new story of ergodic theory
・S. Chen and J. Yong -- Solvability of a stochastic linear quadratic optimal control problem
・M. Davis and F. R. Lischka -- Convertible bonds with market risk and credit risk
・F. J. Hickernell and H. S. Hong -- Quasi-Monte Carlo methods and their randomizations
・H. Yu and Y.-K. Kwok -- Contingent claim approach for analyzing the credit risk of defaultable currency swaps
・S. Luo and Q. Zhang -- Dynamic insider trading
・S. Tang -- A new hedging model and a nonlinear generalization of Black-Scholes formula
・J.-a. Yan -- An overview on the Martingale approach to option pricing
・X. Zhang -- On comparison theorems for diffusion processes
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 26
Publication Year: 2002
ISBN: 0-8218-3191-7
Paging: 148 pp.
Binding: Softcover
Niky Kamran, McGill University, Montreal, QC, Canada
Selected Topics in the Geometrical Study
of Differential Equations
Expected publication date is July 5, 2002
Description
The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. Currently, these ideas occupy a central position in several areas of pure and applied mathematics, including the theory of completely integrable evolution equations, the calculus of variations, and the study of conservation laws. In this book, the author gives an overview of a number of significant ideas and results developed over the past decade in the geometrical study of differential equations.
Topics covered in the book include symmetries of differential equations and variational problems, the variational bi-complex and conservation laws, geometric integrability for hyperbolic equations, transformations of submanifolds and systems of conservation laws, and an introduction to the characteristic cohomology of differential systems.
The exposition is sufficiently elementary so that non-experts can understand the main ideas and results by working independently. The book is also suitable for graduate students and researchers interested in the study of differential equations from a geometric perspective. It can serve nicely as a companion volume to The Geometrical Study of Differential Equations, Volume 285 in the AMS Contemporary Mathematics series.
Contents
・Differential equations and their geometry
・External and generalized symmetries
・Internal, external and generalized symmetries
・Transformations of surfaces
・Tranformations of submanifolds
・Hamiltonian systems of conservation laws
・The variational bi-complex
・The inverse problem of the calculus of variations
・Conservation laws and Darboux integrability
・Characteristic cohomology of differential systems
・Bibliography
Details:
Series: CBMS Regional Conference Series in Mathematics, Number: 96
Publication Year: 2002
ISBN: 0-8218-2639-5
Paging: 115 pp.
Binding: Softcover