The Analytic S-Matrix


Book Description

A theory of the S-Matrix, starting from physically plausible assumptions and looking at the mathematical consequences.




The Analytic S Matrix


Book Description




Introduction to Matrix Analytic Methods in Stochastic Modeling


Book Description

Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.




Monotone Matrix Functions and Analytic Continuation


Book Description

A Pick function is a function that is analytic in the upper half-plane with positive imaginary part. In the first part of this book we try to give a readable account of this class of functions as well as one of the standard proofs of the spectral theorem based on properties of this class. In the remainder of the book we treat a closely related topic: Loewner's theory of monotone matrix functions and his analytic continuation theorem which guarantees that a real function on an interval of the real axis which is a monotone matrix function of arbitrarily high order is the restriction to that interval of a Pick function. In recent years this theorem has been complemented by the Loewner-FitzGerald theorem, giving necessary and sufficient conditions that the continuation provided by Loewner's theorem be univalent. In order that our presentation should be as complete and trans parent as possible, we have adjoined short chapters containing the in formation about reproducing kernels, almost positive matrices and certain classes of conformal mappings needed for our proofs.







Theory Construction and Selection in Modern Physics


Book Description

Analyses what criteria should determine how scientific theories are selected and justified.




Old and New Problems in Elementary Particles


Book Description

Old and New Problems in Elementary Particles provides information pertinent to elementary-particle physics. This book examines the types of problems facing high-energy physicists. Comprised of 20 chapters, this book starts with an overview of the fundamental properties of Dirac poles, with emphasis on the spin, the electric-dipole moment, and the mass. This text then examines the applications of supergain antenna, which is an interesting cautionary model against an oversimplified application of the notion of indeterminacy. Other chapters explain the uninhibited adoption of a uniform and natural experimental definition of resonance or particle with respect to hadrons. This book illustrates as well how insight into strong-interaction dynamics may be improved by a precise definition of the particle-resonance concept. The final chapter deals with the derivation of the Alder–Weisberger relation, which links the ratio of the two weak coupling constants of the nucleon with an integral over pion absorption cross-sections. Physicists and researchers will find this book useful.




Orbiting the Moons of Pluto


Book Description

The Maxwell, Einstein, Schr”dinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space through all of the main equations of Physics should help tighten the noose on ?the? fundamental theory. This kind of exploration of higher dimensional spacetime has for the most part been neglected by M-theorists and physicists in general and is taken to its penultimate form here.




The Physics of Quantum Fields


Book Description

A gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult, and emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, while the Feynman path integral is introduced in the second half where it is seen as indispensable for understanding the connection between renormalization and critical as well as non-perturbative phenomena.




Encyclopaedia of Mathematics


Book Description

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.