Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods...
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, ...
Dynamical scaling is key to our understanding of far from equilibrium relaxation. Where Volume 1 of this set covered the statics and dynamics of transitions into an absorbing state, this one treats relaxation phenomena far from equilibrium and ageing.
Dynamical scaling is key to our understanding of far from equilibrium relaxation. Where Volume 1 of this set covered the statics and dynamics of tr...
Physics and mathematics students are as eager as ever to become acquainted withthefoundationsofgeneralrelativityandsomeofitsmajorapplicationsin astrophysics and cosmology. I hope that this textbook gives a comprehensive and timelyintroduction toboth aspectsof thisfascinating?eld, and willturn out to be useful for undergraduate and graduate students. This book is a complete revision and extension of my previous volume GeneralRelativityandRelativisticAstrophysics thatappearedabouttwenty years ago in the Springer Series Texts and Monographs in Physics; however, it cannot be regarded just as a...
Physics and mathematics students are as eager as ever to become acquainted withthefoundationsofgeneralrelativityandsomeofitsmajorapplicationsin astrop...
Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods...
Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geomet...
The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are...
The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the bo...
Theoretical physics deals with physical models. The main requirements for a good physical model are simplicity and universality. Universal models which can be applied to describe a variety of different phenomena are very rare in physics and, therefore, they are of key importance. Such models attract the special attention of researchers as they can be used to describe underlying physical concepts in a simple way. Such models appear again and again over the years and in various forms, thus extending their applicability and educa tional value. The simplest example of this kind is the model of a...
Theoretical physics deals with physical models. The main requirements for a good physical model are simplicity and universality. Universal models whic...
Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systema...
This book is concerned with relativistic quantum field theory, especially QED, its most successful example. It is set in the no-man's land between the math ematically rigorous but numerically barren general field theory of the math ematical physicist and the computationally fertile but mathematically some times adventurous field theory of the more phenomenologically inclined, and it aims at demonstrating that closer contact between these two disparate cultures may be of benefit to both. Perturbative QED serves as an exam ple. It is shown how the rules of perturbative quantum field theory, one...
This book is concerned with relativistic quantum field theory, especially QED, its most successful example. It is set in the no-man's land between the...
In this book the author extends the concepts introduced in his Quantum Field Theory in Condensed Matter Physics to situations in which the strong electronic correlations are crucial for the understanding of the observed phenomena. Starting from a model field theory to illustrate the basic ideas, more complex systems are analyzed in turn. A special chapter is devoted to the description of antiferromagnets, doped Mott insulators, and quantum Hall liquids from the point of view of gauge theory.
In this book the author extends the concepts introduced in his Quantum Field Theory in Condensed Matter Physics to situations in which the stro...
The imagination is struck by the substantial conceptual identity between the problems met in the theoretical study of physical phenomena. It is absolutely unexpected and surprising, whether one studies equilibrium statistical me- chanics, or quantum field theory, or solid state physics, or celestial mechanics, harmonic analysis, elasticity, general relativity or fluid mechanics and chaos in turbulence. So when in 1988 I was made chair of Fluid Mechanics at the Universita La Sapienza, not out of recognition of work I did on the subject (there was none) but, rather, to avoid my teaching...
The imagination is struck by the substantial conceptual identity between the problems met in the theoretical study of physical phenomena. It is absolu...
