Bücher der Reihe Theoretical and Mathematical Physics

Clearly structured in an intuitive way, this volume provides and overview of relativistic quantum mechanics. A thorough discussion of the one particle concept within relativistic quantum mechanics, including its limitations, is provided.

This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached.

This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required.

From the reviews:"...useful for experts in mathematical physics...this is a very interesting book, which deserves to be found in any physical library." (OPTICS & PHOTONICS NEWS, July/August 2005).

This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories.

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of variousmodels with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

Study Edition

Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Since the appearance of these standard texts many books (both physical and mathematical) on the non relativistic Schrodinger equation have been published, but only very few on the Dirac equation.

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics.

The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others.

First published in 1983, F.J. Yndurain's book on Quantum Chromodynamics has become a classic among advanced textbooks. The new fourth edition maintains the high standard of its predecessors, expanding and improving on the previous edition and presenting new material.

This book offers a modern way of dealing with the problems of equilibrium states of Bose systems. It provides new ways of looking at existing problems, new technologies for solving old problems and new applications for new exact results.

This edition differs from the second chiefly in the addition of about tOO pages devoted to the quantum (or geometric, or Berry) phase, a subject that did not exist when this book was written.

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.

This monograph treats an extensively developed field in modern mathematical physics - the theory of generalized coherent states and their applications to various physical problems. A number of examples from various areas of theoretical and mathematical physics illustrate advantages of this approach, in Part III.

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space.

Focusing on the links connecting statistical and continuum mechanics, this book introduces both theories before leading on to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

From Nucleons to Nucleus deals with single-particle and collective features of spherical nuclei. The book is based on lectures on nuclear physics given by the author. Its main scope is thus to serve as a textbook for advanced students.

The study of dynamical systems is a well established field. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.

This popular, often cited text returns in a softcover edition to provide a thorough introduction to statistical physics and thermodynamics, and to exhibit the universality of the chain of ideas leading from the laws of microphysics to the macroscopic behaviour of matter.

This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.

This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come.

The reader is assumed to be familiar with ordinary nonrelativistic quantum mechanics as presented, e.g., in the following books: Quantum Mechanics, by L.1. An introductory chapter deals with special relativity, of such funda mental importance for particle physics, which most ofthe time is high energy, i.e., highly relativistic physics.

This monograph presents time-dependant methods for studying problems of scattering theory in classical and quantum mechanics. Particular attention is paid to long-range potentials and the text explains the analogy between classical and quantum scattering theory.

This novel approach is presented for the first time in book form. The author demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way.

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.

This useful text provides a survey of the current state of research into the physics of neutrinos. It gives a global view of the areas of physics in which neutrinos play important roles, including astrophysics and cosmology.

This monograph is the first to present the recently discovered renormalization techniques for the Schroedinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject.

Here is a treatise on the thermodynamic and dynamic properties of thin liquid films at solid surfaces, particularly their rupture instabilities. The authors balance 'light' and 'rigorous' mathematical approaches, always conveying the elegance of the theory.