Floyd Williams - Böcker

Such theories as quantum fields and strings have had a fruitful impact on certain developments in mathematics and have the sparked the interests of mathematicians towards a further understanding of some of the basic elements of these physical theories. This monograph navigates through the basic elements of quantum mechanics for a readership of mathematical researchers and graduate students whose background in physics might be rather modest. It should also be of interest to students and researchers in physics. Features include: topics such as Feynman path integrals, quantum statistical partition functions, high and low temperature asymptotics of quantum fields over a negatively curved space-time; a systematic application of the Nikiforov-Uvarov theory of generalised hypergeometric differential equations to solve the Schrodinger equation and to obtain the quantization of energies from a single elegant point of view; application of zeta functions, the Jacobi inversion formula, spherical harmonic analysis and the Selberg trade formula.

Quantum mechanics and quantum field theory are highly successful physical theo­ ries that have numerous practical applications. Largely mathematical in character, these theories continue to stimulate the imaginations of applied mathematicians and purists as weIl. In recent years, in particular, as a new array of tools have emerged, including a representative amount from the domain of so-called pure mathematics, interest in both the conceptual and physical aspects of these beau­ tiful subjects has especially blossomed. Given the emergence of newer and of­ ten spectacular applications of mathematics to quantum theory, and to theoretical physics in general, one notes that certain communication gaps between physicists and mathematicians continue to be bridged. This text on quantum mechanics, designed primarily for mathematics students and researchers, is an attempt to bridge further gaps. Although the mathematical style presented is generally precise, it is counterbalanced at some points by a re­ laxation of precision, as our overall purpose is to capture the basic fiavor of the subject both formally and intuitively. The approach is one in which we attempt to maintain sensitivity with respect to diverse backgrounds of the readers, including those with modest backgrounds in physics. Thus we have included several con­ crete computational examples to fortify stated principles, several appendices, and certain basic physical concepts that help to provide for a reasonably self-contained account of the material, especially in the first 11 chapters.

The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.