Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the ...
One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework. This text introduces precisely such a broad mathematical model, one that gives a clear geometric expression of the symmetry of physical laws and is entirely determined by that symmetry.The first three chapters discuss the occurrence of bounded symmetric domains (BSDs) or homogeneous balls and their algebraic structure in physics. The book further provides a discussion of how to obtain a triple algebraic structure...
One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within...
This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss Theorema Egregium. This theorem expresses the curvature of a...
This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The boo...
This treasure of popular science by the Russian biophysicist Mikhail V. Volkenstein is at last, more than twenty years after its appearance in Russian, available in English translation.
As its title Entropy and Information suggests, the book deals with the thermodynamical concept of entropy and its interpretation in terms of information theory. The author shows how entropy is not to be considered a mere shadow of the central physical concept of energy, but more appropriately as a leading player in all of the major natural processes: physical, chemical, biological, evolutionary, and even...
This treasure of popular science by the Russian biophysicist Mikhail V. Volkenstein is at last, more than twenty years after its appearance in Russ...
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate...
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author s ...
It has been sixteen years since the unification of electro- Magnetism with the weak interactions was developed by Glashow, Salam, and Weinberg. Well before that proposal was fully confirmed by experiment, work began on unifying strong interactions with the electroweak. Now there is a growing effort to incorporate some theory of quantum gravity into the scheme. This enormous complex of theoreti- cal and experimental efforts was the subject of the Fourth Workshop on Grand Unification held in Philadelphia and attended by over two hundred physicists. During the workshop, experimental and...
It has been sixteen years since the unification of electro- Magnetism with the weak interactions was developed by Glashow, Salam, and Weinberg. Well b...
This new volume in the Poincare Seminar Series, describing recent developments at the interface between physics and biology, is directed towards a broad audience of physicists, biologists, and mathematicians. Both the theoretical and experimental aspects are covered, and particular care is devoted to the pedagogical nature of the presentations. The first survey article, by Jean-Francois Joanny and Jacques Prost, describes the theoretical advances made in the study of "active gels," with applications to liquid crystals and cell motility. Jasper van der Gucht and Cecile Sykes then report on...
This new volume in the Poincare Seminar Series, describing recent developments at the interface between physics and biology, is directed towards a bro...
Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang-Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any...
Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an eleme...
This volume of the Poincare Seminar Series covers a key frontier in statistical physics, exploring leading-edge research on the related but little understood topics of glasses--especially the glass transition--and the statics and dynamics of granular systems. Originates in lectures to a broad scientific audience. Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad...
This volume of the Poincare Seminar Series covers a key frontier in statistical physics, exploring leading-edge research on the related but little und...
