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  3. Cambridge Monographs on Mathematical Physics

This highly acclaimed series of monographs provides introductory accounts of specialised topics in mathematical and theoretical physics for graduate students and research workers. The monographs in this series are of outstanding scholarship and written by those at the very frontiers of research. Subject areas covered include cosmology, astrophysics, relativity theory, particle physics, quantum theory, nuclear physics, statistical mechanics, condensed matter physics, plasma physics, and the theory of chaos.

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110 results in Cambridge Monographs on Mathematical Physics

Page 4 of 6

Quantum Field Theory in Curved Spacetime
  • Quantized Fields and Gravity
  • Leonard Parker, David Toms
  • Published online:
    25 January 2011
    Print publication:
    20 August 2009
  • Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.

Non-Perturbative Field Theory
  • From Two Dimensional Conformal Field Theory to QCD in Four Dimensions
  • Yitzhak Frishman, Jacob Sonnenschein
  • Published online:
    07 September 2010
    Print publication:
    08 April 2010
  • Providing a new perspective on quantum field theory, this book gives a pedagogical and up-to-date exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research work in theoretical physics. It describes in detail non-perturbative methods in quantum field theory, and explores two- dimensional and four- dimensional gauge dynamics using those methods. The book concludes with a summary emphasizing the interplay between two- and four- dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics (QCD) in particular, are thoroughly described.

Quantum Inverse Scattering Method and Correlation Functions
  • V. E. Korepin, N. M. Bogoliubov, A. G. Izergin
  • Published online:
    04 August 2010
    Print publication:
    19 August 1993
  • The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians. The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results. The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

Modern Canonical Quantum General Relativity
  • Thomas Thiemann
  • Published online:
    04 August 2010
    Print publication:
    13 September 2007
  • Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.

Scattering from Black Holes
  • J. A. H. Futterman, F. A. Handler, Richard Alfred Matzner
  • Published online:
    04 August 2010
    Print publication:
    31 March 1988
  • This book investigates the propagation of waves in the presence of black holes. Astrophysical black holes may eventually be probed by these techniques. 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. High and low energy limiting cases are treated extensively and semi-classical results are also obtained. The analogy between Newtonian gravitational scattering and Coulomb quantum mechanical scattering is fully exploited. The book introduces the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical black hole. It then develops the formalism of spin-weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic and gravitational scattering. Research workers and graduate and advanced undergraduate students in scattering theory, wave propagation and relativity will find this a comprehensive treatment of the topic.

Causality, Measurement Theory and the Differentiable Structure of Space-Time
  • R. N. Sen
  • Published online:
    04 August 2010
    Print publication:
    11 February 2010
  • Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

Quantum Gravity
  • Carlo Rovelli
  • Published online:
    06 July 2010
    Print publication:
    15 November 2004
  • Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Thermal Field Theory
  • Michel Le Bellac
  • Published online:
    05 May 2010
    Print publication:
    01 August 1996
  • Now in paperback, this text introduces the theoretical framework for describing the quark-gluon plasma, an important new state of matter. The first part of this book is a self-contained introduction to relativistic thermal field theory. Topics include the path integral approach, the real and the imaginary time formalisms, fermion fields and gauge fields at finite temperature. Useful techniques such as the evaluation of frequency sums or the use of cutting rules are illustrated on various examples. The second part of the book is devoted to recent developments, giving a detailed account of collective excitations (bosonic and fermionic), and showing how they give rise to energy scales which imply a reorganization of perturbation theory. The relation with kinetic theory is also explained. Applications to processes which occur in heavy ion collisions and in astrophysics are worked out in detail. Each chapter ends with exercises and a guide to the literature.

Renormalization
  • An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion
  • John C. Collins
  • Published online:
    10 March 2010
    Print publication:
    15 November 1984
  • Most of the numerical predictions of experimental phenomena in particle physics over the last decade have been made possible by the discovery and exploitation of the simplifications that can happen when phenomena are investigated on short distance and time scales. This book provides a coherent exposition of the techniques underlying these calculations. After reminding the reader of some basic properties of field theories, examples are used to explain the problems to be treated. Then the technique of dimensional regularization and the renormalization group. Finally a number of key applications are treated, culminating in the treatment of deeply inelastic scattering.

String Theory
  • Volume 2, Superstring Theory and Beyond
  • Joseph Polchinski
  • Published online:
    26 February 2010
    Print publication:
    13 October 1998
  • String Theory, first published in 1998, comprises two volumes which provide a comprehensive and pedagogic account of the subject. Volume 2 begins with an introduction to supersymmetric string theories and presents the important advances of recent years. The first three chapters introduce the type I, type II, and heterototic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. The final chapters are concerned with four-dimensional string theories, showing how some of the simplest string models connect with previous ideas for unifying the Standard Model. They collect many important results on world-sheet and spacetime symmetries. An appendix summarizes the necessary background on fermions and supersymmetry. An essential text and reference for graduate students and researchers interested in superstring theory.

Gravity and Strings
  • Tomás Ortín
  • Published online:
    20 February 2010
    Print publication:
    25 March 2004
  • One appealing feature of string theory is that it provides a theory of quantum gravity. Gravity and Strings is a self-contained, pedagogical exposition of this theory, its foundations and its basic results. In Part I, the foundations are traced back to the very early special-relativistic field theories of gravity, showing how such theories lead to general relativity. Gauge theories of gravity are then discussed and used to introduce supergravity theories. In Part II, some of the most interesting solutions of general relativity and its generalizations are studied. The final Part presents and studies string theory from the effective action point of view, using the results found earlier in the book as background. This 2004 book will be useful as a reference book for graduate students and researchers, as well as a complementary textbook for courses on gravity, supergravity and string theory.

Quantum Groups in Two-Dimensional Physics
  • Cisar Gómez, Martm Ruiz-Altaba, German Sierra
  • Published online:
    08 February 2010
    Print publication:
    18 April 1996
  • This 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang–Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, giving particular emphasis to vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebra. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text.

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics
  • Josi A. de Azcárraga, Josi M. Izquierdo
  • Published online:
    08 February 2010
    Print publication:
    23 November 1995
  • 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). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.

Exact Space-Times in Einstein's General Relativity
  • Jerry B. Griffiths, Jiří Podolský
  • Published online:
    04 February 2010
    Print publication:
    15 October 2009
  • Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.

Spinors and Space-Time
  • Volume 1, Two-Spinor Calculus and Relativistic Fields
  • Roger Penrose, Wolfgang Rindler
  • Published online:
    03 February 2010
    Print publication:
    18 October 1984
  • 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.

The Large Scale Structure of Space-Time
  • S. W. Hawking, G. F. R. Ellis
  • Published online:
    26 January 2010
    Print publication:
    10 May 1973
  • 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.

Structures in the Universe by Exact Methods
  • Formation, Evolution, Interactions
  • Krzysztof Bolejko, Andrzej Krasiński, Charles Hellaby, Marie-Noëlle Célérier
  • Published online:
    20 January 2010
    Print publication:
    22 October 2009
  • As the structures in our Universe are mapped out on ever larger scales, and with increasing detail, the use of inhomogeneous models is becoming an essential tool for analyzing and understanding them. This book reviews a number of important developments in the application of inhomogeneous solutions of Einstein's field equations to cosmology. It shows how inhomogeneous models can be employed to study the evolution of structures such as galaxy clusters and galaxies with central black holes, and to account for cosmological observations like supernovae dimming, the cosmic microwave background, baryon acoustic oscillations or the dependence of the Hubble parameter on redshift within classical general relativity. Whatever `dark matter' and `dark energy' turn out to be, inhomogeneities exist on many scales and need to be investigated with all appropriate methods. This book is of great value to all astrophysicists and researchers working in cosmology, from graduate students to academic researchers.

Liquid Metals
  • Concepts and Theory
  • Norman Henry March
  • Published online:
    19 January 2010
    Print publication:
    26 October 1990
  • 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. The quantitative theory of liquid pair correlation functions, effective ion-ion interactions, thermodynamic properties and electronic and atomic transport is then developed. The book goes on to discuss inelastic neutron scattering, critical behaviour, magnetism, the liquid/metal surface, binary liquid metal alloys, the two component theory of pure liquid metals, shock wave studies, liquid hydrogen plasmas and the constitution of giant planets.

Gauge Field Theories
  • 2nd edition
  • Stefan Pokorski
  • Published online:
    13 January 2010
    Print publication:
    28 February 2000
  • Quantum field theory forms the present theoretical framework for our understanding of the fundamental interactions of particle physics. This up-dated and expanded text examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. Beginning with a new chapter giving a systematic introduction to classical field theories and a short discussion of their canonical quantization and the discrete symmetries C, P and T, the book provides a brief exposition of perturbation theory, the renormalization programme, and the use of the renormalization group equation. It then explores topics of current research interest including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry. A chapter on basics of the electroweak theory is now included. Professor Pokorski, a distinguished theoretical physicist, has presented here a self-contained text for graduate courses in physics; the only prerequisite is some grounding in quantum field theory.

Topological Solitons
  • Nicholas Manton, Paul Sutcliffe
  • Published online:
    12 January 2010
    Print publication:
    10 June 2004
  • Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.

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