Books in the Cambridge Monographs on Mathematical Physics series

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.

This monograph, originally published in 1980, seeks to provide an introduction to high-energy model making. Its aim is to explain the basic ideas in a form accessible to graduate students and other readers who have acquired a first-hand knowledge of quantum field theory and basic particle physics, including the elements of Regge theory.

This book describes the theory and select applications of one of the most important mathematical tools used in theoretical investigations of collective excitations in statistical physics, such as occur in superfluidity, superconductivity, plasma dynamics, superradiation, and in phase transitions.

This book, originally published in 2006, describes the general theory of Moonshine and its underlying concepts, emphasising the fundamental ideas and examples behind some of the most fascinating topics in mathematics and physics. For graduates and researchers working in areas such as algebra, number theory, geometry, analysis, quantum field theory and conformal field theory.

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in quantum mechanics.

This book describes the theory of semi simple and affine Lie algebras, and of quantum groups. Various applications of these theories to two-dimensional conformal field theories are presented. In particular, the link between affine Lie algebras and quantum groups arising in this context is described.

This is a modern self-contained introduction to key topics in advanced general relativity. Exercises are included.

This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

This 2002 book provides a thorough introduction to quantum theory of gauge fields, with emphasis on non-perturbative methods. Suitable as a textbook for advanced graduate courses in quantum field theory, it will also be of interest to researchers in high energy theory and condensed matter physics.

This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.

Describes present knowledge of protons and neutrons, the particles which make up the nucleus of the atom. Experiments using high energy electrons, muons and neutrinos reveal the proton as being made up of point-like constituents, quarks. The strong forces binding quarks together are detailed.

This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research.

This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research.

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 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. It covers S-matrices, spin chains, vertex models, Yang-Baxter algebras, the Bethe ansatz, quantum groups, integrable models, two-dimensional conformal field theories and superconformal field theories. Many diagrams and exercises are included.

Liquid metals remain of both fundamental and technological interest and the concepts needed to understand their properties are set out in this book, starting from a survey of the basic experimental facts to be explained.

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.