Books in the Cambridge Monographs on Mathematical Physics series

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

Scientists have been debating the meaning of quantum mechanics for over a century. This book for graduate students and researchers gets to the root of the problem; the contextual nature of empirical truth, the laws of observation and how these impact on our understanding of quantum physics. Bridging the gap between non-relativistic quantum mechanics and quantum field theory, this novel approach to quantum mechanics extends the standard formalism to cover the observer and their apparatus. The author demystifies some of the aspects of quantum mechanics that have traditionally been regarded as extraordinary, such as wave-particle duality and quantum superposition, by emphasizing the scientific principles rather than the mathematical modelling involved. Including key experiments and worked examples throughout to encourage the reader to focus on empirically sound concepts, this book avoids metaphysical speculation and also alerts the reader to the use of computer algebra to explore quantum experiments of virtually limitless complexity.

This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kahler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex geometries.

This text introduces the theoretical framework for describing the quark-gluon plasma, an important new state of matter. The first part is a self-contained introduction to the principles of relativistic thermal field theory. The second part details recent developments. Each chapter contains exercises and a guide to the literature.

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics. Here the authors describe some of the most recent and general approaches and include some significant new results.

'This is an excellent book and admirably lives up to the promise implied in its title in giving a thorough treatment of the mathematical structure underlying the theory of general relativity.' T. R. Carson, Observatory

This book gives an account of the properties of the interacting boson model. In particular, this book presents the mathematical techniques used to analyze the structure of the model.

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

This book surveys the physics of small clusters of particles undergoing vibrations, with applications in nuclear physics and the physics and chemistry of atomic clusters. It considers experimental information, theoretical tools, the important vibrational modes, damping mechanisms and excitation energy.

The first comprehensive survey of (2+1)-dimensional quantum gravity. It presents some fifteen different approaches, comparing the resulting theories and suggesting implications for the ultimate goal of a (3+1)-dimensional theory uniting general relativity and quantum mechanics. An invaluable resource for all graduate students and researchers working in quantum gravity.

The interacting boson model was introduced in 1974 as an attempt to describe collective properties of nuclei in a unified way. Since 1974, the model has been the subject of many investigations and it has been extended to cover most aspects of nuclear structure. This book gives an account of the properties of the interacting boson model.

A comprehensive and coherent introduction to modern quantum cosmology - the study of the universe as a whole according to the laws of quantum mechanics. Ample introductory material is included to ensure it is well suited as a graduate text. Researchers in theoretical and mathematical physics, applied maths and cosmology will also find it of immediate interest.

This 2001 book gives a self-contained exposition of the theory of gravitational solitons and provide a comprehensive review of exact soliton solutions to Einstein's equations. A valuable reference for researchers and graduate students.

This graduate/research level text is a self-contained exposition of the applications of kinetic theory to basic problems in modern cosmology. It studies what can be concluded from the application to cosmological problems of kinetic theory and, in particular, the Boltzmann equation and its solutions.

In Relativistic Fluids and Magneto-fluids there are chapters on mathematical structure, singluar hypersurfaces in space-time, propagation of weak discontinuities, relativistic simple waves, relativistic geometrical optics, relativistic asymptotic waves, relativistic shock waves, and stability of relativistic shock waves.

This graduate/research level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantisation of strings, gravity and topological field theory.

Originally published at the height of the first revolution in string theory, these two volumes went on to define the field. Volume 2 focuses on one-loop amplitudes, anomalies and phenomenology. Featuring a new Preface, this book is invaluable for graduate students and researchers in high energy physics and astrophysics.

This accessible volume provides the cosmological and string-theoretic background necessary to understand inflation in string theory. Presenting a modern treatment of inflationary cosmology and its connections to string theory and elementary particle theory, this is a self-contained resource for graduate students and researchers in string theory, cosmology, and related fields.

The theory of relativity describes the laws of physics in a given space-time. However, a physical theory must provide observational predictions expressed in terms of measurements, which are the outcome of practical experiments and observations. Ideal for readers with a mathematical background and a basic knowledge of relativity, this book will help readers understand the physics behind the mathematical formalism of the theory of relativity. It explores the informative power of the theory of relativity, and highlights its uses in space physics, astrophysics and cosmology. Readers are given the tools to pick out from the mathematical formalism those quantities that have physical meaning and which can therefore be the result of a measurement. The book considers the complications that arise through the interpretation of a measurement, which is dependent on the observer who performs it. Specific examples of this are given to highlight the awkwardness of the problem.

This 1998 volume provides a comprehensive account of the bosonic string, introducing the central ideas of string theory, based on the Polyakov path integral and conformal field theory. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.

A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

This 1998 volume provides a comprehensive introduction to supersymmetric string theories, presents important discoveries that have been made including D-branes, and goes on to discuss four-dimensional string theories. This is an essential text and reference for graduate students and researchers interested in superstring theory.

This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

This 1998 volume provides a comprehensive account of the bosonic string, introducing the central ideas of string theory, based on the Polyakov path integral and conformal field theory. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.

In this thorough and coherent introduction to tau functions, Harnad and Balogh start with the basics and extend right through to the most recent research results. This monograph is ideal for graduates or researchers in related fields unacquainted with the full range of applications of the theory of tau functions.

Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail).

A comprehensive and coherent account of the theory of quantum fields on a lattice. It includes chapters on scalar fields, gauge fields and fermion fields, quarks and gluons in QCD and fermions and bosons in the electroweak theory and numerical simulation algorithms.

This book investigates the propagation of waves in the presence of black holes. The authors emphasise intuitive physical thinking in their treatment of the techniques of analysis of scattering, but alternate this with chapters on the rigourous mathematical development of the subject.

Just as ordinary symmetries relate various forms of matter to each other, and various basic forces to each other, so the novel concept of supersymmetry relates (Fermi) matter to (Bose) force. This book provides a brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories.

This text describes the gravitational interactions and evolution of astronomical systems on all scales, from small groups of stars through galaxies and clusters of galaxies to the Universe itself. It is written to bring out the physical content behind the mathematical formulae, and contains a number of exercises and suggestions for research topics.