Bøker i Theoretical and Mathematical Physics-serien

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 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.

For the past five years, my editor at Springer-Verlag has asked me to write a second edition of this text that would incorporate new material on the quark model.

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.

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.

In this textbook for graduate students in physics the author carefully analyses the role of causality in Q.E.D. The extension of the methods to non-abelian gauge theories is briefly described. The book differs considerably from its first edition: Chap. 3 on Causal Perturbation Theory was completely rewritten and Chap.

This book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of parti cle physics.

Here we demonstrate how microscopic collision processes (that is, processes which can be described by quantum mechanics) can be used to obtain novel preparation and registration procedures if we take for granted the knowledge of only a few macroscopic preparation and registration procedures.

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.

This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system.

Study Edition

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.

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

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.

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.

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 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.

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.

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.