This volume links field theory methods and concepts from
particle physics with those in critical phenomena and statistical
mechanics, the development starting from the latter point of view.
Rigor and lengthy proofs are trimmed by using the
phenomenological framework of graphs, power counting, etc., and
field theoretic methods with emphasis on renormalization group
techniques. Non-perturbative methods and numerical simulations
are introduced in this new edition. Abundant references to
research literature complement this matter-of-fact approach. The
book introduces quantum field theory to those already grounded in
the concepts of statistical mechanics and advanced quantum
theory, with sufficient exercises in each chapter for use as a
textbook in a one-semester graduate course.
The following new chapters are included:
I. Real Space Methods
II. Finite Size Scaling
III. Monte Carlo Methods. Numerical Field Theory
Contents:
Pertinent Concepts and Ideas in the Theory of Critical Phenomena
Formulation of the Problem of Phase Transitions in Terms of
Functional Integrals
Functional Integrals in Quantum Field Theory
Perturbation Theory and Feynman Graphs
Vertex Functions and Symmetry Breaking
Expansions in the Number of Loops and Components
Renormalization
The Renormalization Group and Scaling the Critical Region
The Computation of the Critical Exponents
Beyond Leading Scaling
Universality Revisited
Critical Behavior with Several Couplings
Crossover Phenomena
Critical Phenomena near Two Dimensions
Real Space Methods
Finite Size Scaling
Monte Carlo Methods. Numerical Field Theory
Readership: Students and researchers in high energy physics,
computational physics, condensed matter physics, computational
chemistry and theoretical chemistry.
Reviews of the 2nd Edition
gRecommended as the core text for any introductory course on
field theory.h
American Scientists (USA)
gThere are only very few textbooks on the intermediate level,
and the first edition of Amit's work has been a very useful one.
The second edition with a detailed exposition on finite size
scaling, universality and the critical behavior with several
coupling constants promises to be a valuable tool in the library
of many physicists.h
Journal of Applied Mathematics and Physics, Switzerland
600pp (approx.) Pub. date: Scheduled Summer 2005
ISBN 981-256-109-9
ISBN 981-256-119-6(pbk)
Series on Knots and Everything
The physical properties of knotted and linked configurations in
space have been of interest to physicists and mathematicians for
a long time. More recently and more widely, they have become
interesting to biologists and physicists, and to engineers among
others. The depth of importance and breadth of application are
now widely appreciated.
In this volume, there are several contributions from researchers
who are using computers to study problems that would otherwise be
intractable. While computations have long been used to analyze
problems, formulate conjectures, and search for special
structures in knot theory, increased computational power has made
them a staple in many facets of the field. From properties of
knot invariants, to knot tabulation, studies of hyperbolic
structures, knot energies, and the exploration of spaces of
knots, computers have opened the doors to problems that would
have otherwise been too difficult to do by hand computation.
There are also contributions concentrating on models that
researchers use to understand knotting, linking, and entanglement
in physical and biological systems. Topics range from knotted
umbilical cords, to studies of DNA knots and knots in proteins to
the structure of tight knots.
Contents:
Physical Knot Theory:
Universal Energy Spectrum of Tight Knots and Links in Physics (R
Buniy & T Kephart)
Biarcs, Global Radius of Curvature, and the Computation of Ideal
Knot Shapes (M Carlen et al.)
A Tutorial on Knot Energies (E J J van Rensburg)
Knot Theory in the Life Sciences:
Folding Complexity in a Random-Walk Copolymer Model (G Arteca)
Protein Folds, Knots and Tangles (W Taylor)
Monte Carlo Simulations of Gel-Electrophoresis of DNA Knots (C
Weber et al.)
Knotted Umbilical Cords (A Goriely)
Computational Knot Theory:
Ropelength of Tight Polygonal Knots (J Baranska et al.)
Topological Entropic Force Between a Pair of Random Knots Forming
a Fixed Link (T Deguchi)
Universal Characteristics of Polygonal Knot Probabilities (K
Millett & E Rawdon)
Geometric Knot Theory:
Quadrisecants of Knots with Small Crossing Number (G T Jin)
Minimal Flat Knotted Ribbons (L Kauffman)
Conjectures on the Enumeration of Alternating Links (P Zinn-Justin)
and other papers
Readership: Researchers in geometry, topology, numerical &
computational mathematics, molecular biology and physics, and
medical doctors.
530pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 981-256-187-0
In the history of physics and science, quantum mechanics has
served as the foundation of modern science. This book discusses
the properties of microscopic particles in nonlinear systems,
principles of the nonlinear quantum mechanical theory, and its
applications in condensed matter, polymers and biological systems.
The book is essentially composed of three parts. The first part
presents a review of linear quantum mechanics, as well as
theoretical and experimental fundamentals that establish the
nonlinear quantum mechanical theory. The theory itself and its
essential features are covered in the second part. In the final
part, extensive applications of this theory in physics, biology
and polymer are introduced. The whole volume forms a complete
system of nonlinear quantum mechanics.
The book is intended for researchers, graduate students as well
as upper-level undergraduates.
Contents:
Linear Quantum Mechanics (LQM): Its Successes and Problems
Macroscopic Quantum Effects and Properties of Motion of
Quasiparticles
The Fundamental Principles and Theories of Nonlinear Quantum
Mechanics
Wave-Corpuscle Duality of Microscopic Particles (MIP) in the NLQM
Nonlinear Interaction and Localization of the MIP
Nonlinear Versus Linear Quantum Mechanics
The Problems Solving in the NLQM
Properties and States of the MIP in Different Nonlinear Systems
Nonlinearly Quantum-Mechanical Properties of the Excitons and
Phonons
Properties of Nonlinear Excitations and Motions for Protons,
Polarons and Magnons in Different Systems
Readership: Graduates and researchers in the fields of nonlinear
science, quantum, theoretical and condensed matter physics.
650pp (approx.) Pub. date: Scheduled Summer 2005
ISBN 981-256-116-1
ISBN 981-256-299-0(pbk)
In the past three decades, studies on the Painleve equations
have rapidly developed through the efforts of many researchers in
various fields. The Painleve equations have numerous applications
to differential geometry, probability theory, soliton theory,
topological field theory, and others. In the past ten years, the
Painleve equations have been studied not only by analytic
methods, but also by algebraic methods, such as rational
algebraic surfaces, differential Galois theory, the affine Weyl
groups, and representation theory.
This book serves as a guide to algebraic studies on the Painleve
equations and as an introduction to non-specialists. The book
aims to be self-contained by presenting complete proofs of the
theorems.
Contents:
Nonlinear Differential Equations with No Movable Singularities
Isomonodromy Deformations
Initial Value Spaces
Backlund Transformations
Ñ Functions and Bilinear Equations
Irreducibility
Special Solutions
Discrete Painleve Equations
Noumi?Yamada Systems (Dressing Chain)
Readership: Graduates and researchers in analysis and
differential equations, and mathematical physics.
350pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 981-256-194-3
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s?1970s).
This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevofs textbook, some of which are of great importance but are not available now.
The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Contents:
Hypothesis Testing
Quantum Cramer-Rao Bound in Mixed States Model
Quantum Cramer-Rao Bound in Pure States Model
Group Symmetric Approach to Pure States Model
Large Deviation Theory in Quantum Estimation
Futher Topics on Quantum Statistical Inference
Readership: Graduate students in quantum physics, mathematical physics, and probability and statistics.
560pp Pub. date: Feb 2005
ISBN 981-256-015-7
Series: Graduate Texts in Mathematics, Vol. 185
2005, X, 592 p. 24 illus.,
ISBN: 0-387-20706-6/ Hardcover
ISBN: 0-387-20733-3/ Softcover
About this textbook
For this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text.
In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grobner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text.
Table of contents
Introduction.- Solving Polynomial Equations.- Resultants.- Computation in Local Rings.- Modules.- Free Resolutions.- Polytopes, Resultants and Equations.- Integer Programming, Combinatorics and Splines.- Algebraic Coding Theory.- The Berlekamp-Massey-Sakata Decoding Algorithm.