Yakov M. Shnir – författare

Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.

This monograph addresses the field theoretical aspects of magnetic monopoles. Written for graduate students as well as researchers, the author demonstrates the interplay between mathematics and physics. He delves into details as necessary and develops many techniques that find applications in modern theoretical physics. This introduction to the basic ideas used for the description and construction of monopoles is also the first coherent presentation of the concept of magnetic monopoles. It arises in many different contexts in modern theoretical physics, from classical mechanics and electrodynamics to multidimensional branes. The book summarizes the present status of the theory and gives an extensive but carefully selected bibliography on the subject. The first part deals with the Dirac Monopole, followed in part two by the monopole in non-abelian gauge theories. The third part is devoted to monopoles in supersymmetric Yang-Mills Theories.

It seemstoberelatedtothesymmetryoftheobject.Fromaphysicalviewpoint, this de?nition is very attractive: it allows us to describe a central concept of theoretical physics over the last two centuries as being a quest for higher symmetry of Nature.

Quantum systems in all areas of physics, from atomic and molecular physics, nuclear and particle physics to condensed matter and astrophysics, provide a rich mosaic of different structures. Yet there are some simple and universal working principles of nature which seem to govern these structures and manifest themselves in various forms, as well as likely hypothetical ones which might do the same. For example, the same symmetry group structure occurs again and again in optics, atomic physics and particle physics. Concepts like potential, phases, bound states, tunneling, interference, solitons, radiation and resonance are universal.It is for those reasons that a collection of recent works in the many areas of physics on quantum structures and the methods for their investigation is important. The present volume fulfills this task to a large extent. The contributions are wide-ranging and yet there is a certain continuity. The main topics, namely non-perturbative methods in quantum theory, quantum nonlinear systems, quantum phases and magnetic monopoles, are covered by longer review articles and are enriched by many related contributions. It is also very appropriate that the corresponding mathematical methods, such as those for solving Schrödinger and relativistic wave equations, as well as those of algebra and group representations and analysis, are included in this volume.