Bücher der Reihe Theoretical and Mathematical Physics

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.

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.

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

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.

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.

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 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.

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.

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 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 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.

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.

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 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 thorough volume is the perfect foundation for intermediate-level research in string theory. Its pedagogic and self-contained structure raises is a step up from results compendia and features more advanced topics including conformal field theory.

"Many-Body Problems and Quantum Field 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.

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds.

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;

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 various models 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.

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.

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.

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.).

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.

This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

The book gives an exposition of the standard model of elementary particles based on coordinate-free differential geometric foundations. It addresses students in physics and mathematics.