Books in the Theoretical and Mathematical Physics series

Intended as a compendium for physicists and mathematicians on coherent states and their applications, this volume moves from the basic mathematical structures of generalized coherent states to specific examples of coherent states such as the hydrogen atom.

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.

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.

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.

Critical phenomena arise in a wide variety of physical systems. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments.

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 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.

From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [...] It will be very useful for both mathematicians and physicists." EMS Newsletter

In retrospect, the first edition of this book now seems like a mere sketch for a book. Among the more obvious changes, this edition contains a new section on Kruskal space, another on the plane gravitational wave, and a third on linearized general relativity;

In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.

This is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom.

Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry, as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods.

Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.

This monograph on fluid mechanics is not only a superb and unique textbook but also an impressive piece of research. It is the only textbook that fully covers turbulence, all the way from the works of Kolmogorov to modern dynamics.

"Many-Body Problems and Quantum Field Theory".

Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles.

The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

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).

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.