V.K. Balachandran, Ramanujan Institute for Advanced Studies in Mathematics, Chennai, India.
Topological Algebras
Included in series
North-Holland Mathematics Studies, 185
Description
This book consists of nine chapters. Chapter 1 is devoted to algebraic preliminaries. Chapter 2 deals with some of the basic definition and results concerning topological groups, topological linear spaces and topological algebras. Chapter 3 considered some generalizations of the norm. Chapter 4 is concerned with a generalization of the notion of convexity called p-convexity. In Chapter 5 some differential and integral analysis involving vector valued functions is developed. Chapter 6 is concerned with spectral analysis and applications. The Gelfand representation theory is the subject-matter of Chapter 7. Chapter 8 deals with
commutative topological algebras. Finally in Chapter 9 an exposition of the norm uniqueness theorems of Gelfand and Johnson (extended to p-Banach algebras) is given.
Contents
Chapter 1: Algebraic Preliminaries
Chapter 2: Topological Preliminaries
Chapter 3: Some Type of Topological Algebras
Chapter 4: Locally Pseudo-Convex Spaces and Algebras
Chapter 5: Some Analysis
Chapter 6: Spectral Analysis in Topological Algebras
Chapter 7: Gelfand Representation Theory
Chapter 8: Commutative Topological Algebras
Chapter 9: Norm Uniqueness Theorems
Appendix. Type Chart. Biliography. Index. List of Special Symbols. List of Special Abbreviations.
Year 2000
Hardbound
ISBN: 0-444-50609-8
452 pages
R. Carroll, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Quantum Theory, Deformation and Integrability
Included in series
North-Holland Mathematics Studies, 186
Description
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will
be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to
understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.
Contents
1. QUANTIZATION AND INTEGRABILITY
1.1 Algebraic and Geometric Methods
1.2 Vertex Operators and Coherent States
1.3 Remarks on the Olavo Theory
1.4 Trajectory Representations
1.5 Miscellaneous
2. GEOMETRY AND EMBEDDING
2.1 Curves and Surfaces
2.2 Surfaces in R3 and Conformal Immersion
2.3 Quantum Mechanics on Embedded Objects
2.4 Willmore Surfaces, Strings and Dirac
2.5 Conformal Maps and Curves
3. CLASSICAL AND QUANTUM INTEGRABILITY
3.1 Background
3.2 R Matrices and PL Structures
3.3 Quantization and Quantum Groups
3.4 Algebraic Bethe Ansatz
3.5 Separation of Variables
3.6 Hirota Equations
3.7 SOV and Hitchin Systems
3.8 Deformation Quantization
3.9 Miscellaneous
3.10 Summary Remarks
4. DISCRETE GEOMETRY AND MOYAL
4.1 Introduction
4.2 Hirota, Strings, and Discrete Surfaces
4.3 A Few Summary Remarks
4.4 More on Phase Space Discretization
5. WHITHAM THEORY
5.1 Background
5.2 Isomonodromy Problems
5.3 Whitham and Seiberg-Witten
5.4 Soft Susy Breaking and Whitham
5.5 Renormalization
5.6 Whitham, WDVV, and Picard-Fuchs
6. GEOMETRY AND DEFORMATION QUANTIZATION
6.1 Noncommutative Geometry
6.2 Gauge Theories
6.3 Berezin Toeplitz Quantization
Bibliography. Index.
Year 2000
Hardbound
ISBN: 0-444-50621-7
420 pages
Hartry Field, Professor of Philosophy, New York University
Truth and the Absence of Fact.
440 pages, 234mm x 156mm
Details
Hardback, 0-19-924171-6
Paperback, 0-19-924289-5
Description
Readership: Professional philosophers, advanced students of philosophy, and logicians.
Hartry Field presents a selection of thirteen of his most important essays on a set of
related topics at the foundations of philosophy; one essay is previously unpublished, and eight are accompanied by substantial new postscripts. Five of the essays are primarily about truth, meaning, and propositional attitudes, five are primarily about semantic indeterminacy and other kinds of 'factual defectiveness' in our discourse, and three are primarily about issues concerning objectivity, especially
in mathematics and in epistemology. This influential work by a key figure in contemporary philosophy will reward the attention of any philosopher interested in language, epistemology, or mathematics.
Contents/contributors
Preface
I. Truth, Meaning and Propositional Attitudes
1 Tarski's Theory of Truth Postscript
2 Mental Representation Postscript
3 Stalnaker on Intentionality
4 Deflationist Theories of Meaning and Content Postscript
5 Attributions of Meaning and Content
II. Indeterminacy and Factual Defectiveness
6 Theory Change and the Indeterminacy of Reference Postscript
7 Quine and the Correspondence Theory Postscript
8 Disquotational Truth and Factually Defective Discourse
9 Some Thoughts on Radical Indeterminacy Postscript
10 Indeterminacy, Degree of Belief, and Excluded Middle Postscript
III. Objectivity
11 Mathematical Objectivity and Mathematical Objects
12 Which Undecidable Sentences Have Determinate Truth Values?
13 Apriority as an Evaluative Notion
Bibliography, Index
Edited by E.R. PikePierre C. Sabatier
Scattering and inverse scattering in pure and applied science
ISBN: 0126137609
Cover: CaseBound
Published: June 2001
Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of
sound in many directions due to irregularities in the transmission medium.
Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by
researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering.
This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research.
Edited by Cornelius T. Leondes
University of California Los Angeles, University of Califfornia San Diego,
and University of Washington
The Technology of Knowledge Management and Decision Making
for the 21st Century
ISBN: 0124438806
Cover: ComBound
Published: October 2001
This six-volume set presents cutting-edge advances and applications of expert systems. Because expert systems combine the expertise of engineers, computer scientists, and computer programmers, each group will benefit from buying this important reference work.
An "expert system" is a knowledge-based computer system that emulates the decision-making ability of a human expert. The primary role of the expert system is to perform appropriate functions under the close supervision of the human, whose work is supported by that expert system. In the reverse, this same expert system can monitor and double check the human in the performance of a task. Human-computer interaction in our highly complex world requires the development of a wide array of expert systems.
Hilborn, R.C., Amherst College, Amherst, MA, USA
Tino, G.M., University of Naples, Italy
(Eds.)
Spin-Statistics Connection and Commutation Relations
Experimental Tests and Theoretical Implications, Anacapri, Capri
Island, Italy 31 May-3 June 2000
2000. X, 322 pp. Hardcover
1-56396-974-2
The conference focused on the issues of the behavior of systems of identical particles in quantum
mechanics. These questions are important in all areas of physics, in much of chemistry (via the
Pauli Exclusion Principle) and mathematics, and in the philosophy of science. The conference
brought together experimentalists, theorists, and philosophers to survey work done during the past
ten years that challenges the traditional view of these issues. Several papers explore connections
with rapidly developing fields such as fundamental symmetries, supersymmetry, quantum gravity,
and quantum computation.
Keywords: Spin physics ; quantum mechanics ; symmetries
Series: AIP Conference Proceedings.VOL. 545
Fields: Condensed Matter and Properties of Materials; Quantum Physics
Written for: Quantum physicists, theoretical physicists, mathematicians concerned
with group theory and quantum algebra, quantum chemists, philosophers of science
Book category: Proceedings
Publication language: English