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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 5 of 6

Relativistic Numerical Hydrodynamics
  • James R. Wilson, Grant J. Mathews
  • Published online:
    11 January 2010
    Print publication:
    06 November 2003
  • This book presents an overview of the computational framework in which calculations of relativistic hydrodynamics have been developed. It summarizes the jargon and methods used in the field, and provides illustrative applications to real physical systems. The authors explain how to break down the complexities of Einstein's equations and fluid dynamics, stressing the viability of the Euler–Lagrange approach to astrophysical problems. The book contains techniques and algorithms enabling one to build computer simulations of relativistic fluid problems for various astrophysical systems in one, two and three dimensions. It also shows the reader how to test relativistic hydrodynamics codes. Suitable for graduate courses on astrophysical hydrodynamics and relativistic astrophysics, this book also provides a valuable reference for researchers already working in the field.

The Theory of Complex Angular Momenta
  • Gribov Lectures on Theoretical Physics
  • V. N. Gribov
  • Published online:
    06 January 2010
    Print publication:
    04 December 2003
  • This 2003 book provides a rigorous introduction to the theory of complex angular momenta, based on the methods of field theory. It comprises an English translation of the series of lectures given by V. N. Gribov in 1969, when the physics of high-energy hadron interactions was being created. Besides their historical significance, these lectures contain material which is highly relevant to research today. The basic physical results and the approaches Gribov developed are now being rediscovered in an alternative context: in the microscopic theory of hadrons provided by quantum chromodynamics. The ideas and calculation techniques presented in this book are useful for analysing high-energy hadron scattering phenomena, deep inelastic lepton-hadron scattering, the physics of heavy ion collisions, kinetic phenomena in phase transitions, and will be instrumental in the analysis of electroweak processes at the next-generation particle accelerators, such as LHC and TESLA.

Relativistic Fluids and Magneto-fluids
  • With Applications in Astrophysics and Plasma Physics
  • A. M. Anile
  • Published online:
    06 January 2010
    Print publication:
    23 February 1990
  • This highly acclaimed series of monographs provides introductory accounts of specialized topics in mathematical 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.

Spinors and Space-Time
  • Volume 2, Spinor and Twistor Methods in Space-Time Geometry
  • Roger Penrose, Wolfgang Rindler
  • Published online:
    23 December 2009
    Print publication:
    27 February 1986
  • In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.

Quantum Gravity in 2+1 Dimensions
  • Steven Carlip
  • Published online:
    15 December 2009
    Print publication:
    02 July 1998
  • This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quantizations are explored, as well as implications for such issues as topology change and the 'problem of time'. This book is an invaluable resource for all graduate students and researchers working in quantum gravity.

Methods of Contemporary Gauge Theory
  • Yuri Makeenko
  • Published online:
    02 December 2009
    Print publication:
    15 August 2002
  • This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

D-Branes
  • Clifford V. Johnson
  • Published online:
    24 November 2009
    Print publication:
    19 December 2002
  • D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting the recent developments and ideas in a pedagogical manner. It is suitable for use as a textbook in graduate courses on modern string theory and theoretical particle physics, and will also be an indispensable reference for seasoned practitioners. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes, uncovering further aspects while actually working with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for other avenues of research.

Advanced General Relativity
  • John Stewart
  • Published online:
    10 November 2009
    Print publication:
    30 August 1991
  • This is a modern self-contained introduction to key topics in advanced general relativity. The opening chapter reviews the subject, with strong emphasis on the geometric structures underlying the theory. The next chapter discusses 2-component spinor theory, its usefulness for describing zero-mass fields, its practical application via Newman-Penrose formalism, together with examples and applications. The subsequent chapter is an account of the asymptotic theory far from a strong gravitational source, describing the mathematical theory by which measurements of the far-field and gravitational radiation emanating from a source can be used to describe the source itself. The final chapter describes the natural characteristic initial value problem, first in general terms, and then with particular emphasis for relativity, concluding with its relation to Arnold's singularity theory. Exercises are included.

Exact Solutions of Einstein's Field Equations
  • 2nd edition
  • Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers, Eduard Herlt
  • Published online:
    10 November 2009
    Print publication:
    27 March 2003
  • 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.

Finite-Temperature Field Theory
  • Principles and Applications
  • 2nd edition
  • Joseph I. Kapusta, Charles Gale
  • Published online:
    04 November 2009
    Print publication:
    03 August 2006
  • The 2006 second edition of this book develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Specific physical theories treated include QED, QCD, electroweak theory, and effective nuclear field theories of hadronic and nuclear matter. Topics include: functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and plasma oscillations, spontaneous symmetry breaking, Goldstone theorem, resummation and hard thermal loops, lattice gauge theory, phase transitions, nucleation theory, quark-gluon plasma, and color superconductivity. Applications to astrophysics and cosmology cover white dwarf and neutron stars, neutrino emissivity, baryon number violation in the early universe, and cosmological phase transitions. Applications to relativistic nucleus-nucleus collisions are also included. The book is written for theorists in elementary particle physics, nuclear physics, astrophysics, and cosmology. Problems are given at the end of each chapter, and numerous references to the literature are included.

Functional Integration
  • Action and Symmetries
  • Pierre Cartier, Cecile DeWitt-Morette
  • Published online:
    04 November 2009
    Print publication:
    30 November 2006
  • Functional integration successfully entered physics as path integrals in the 1942 PhD dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov–Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.

Supersymmetric Quantum Cosmology
  • P. D. D'Eath
  • Published online:
    30 October 2009
    Print publication:
    13 July 1996
  • This volume provides a comprehensive and coherent introduction to modern quantum cosmology - the study of the universe as a whole according to the laws of quantum mechanics. In particular, it presents a useful survey of the many profound consequences of supersymmetry (supergravity) in quantum cosmology. After a general introduction to quantum cosmology, the reader is led through Hamiltonian supergravity and canonical quantization and quantum amplitudes through to models of supersymmetric mini superspace and quantum wormholes. The book is rounded off with a look at exciting further developments, including the possible finiteness of supergravity. Ample introductory material is included, ensuring this topical volume is well suited as a graduate text. Researchers in theoretical and mathematical physics, applied maths and cosmology will also find it of immediate interest.

Path Integrals and Anomalies in Curved Space
  • Fiorenzo Bastianelli, Peter van Nieuwenhuizen
  • Published online:
    28 October 2009
    Print publication:
    20 July 2006
  • 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.

The Schwinger Action Principle and Effective Action
  • David J. Toms
  • Published online:
    27 October 2009
    Print publication:
    15 November 2007
  • This book is an introduction to the Schwinger action principle in quantum mechanics and quantum field theory, with applications to a variety of different models including Bose–Einstein condensation, the Casimir effect and trapped Fermi gases. The book begins with a brief review of the action principle in classical mechanics and classical field theory. It then moves on to quantum field theory, focusing on the effective action method. This is introduced as simply as possible by using the zero-point energy of the simple harmonic oscillator as the starting point. The book concludes with a more complete definition of the effective action, and demonstrates how the provisional definition used earlier is the first term in the systematic loop expansion. The renormalization of interacting scalar field theory is presented to two-loop order. This book will interest graduate students and researchers in theoretical physics who are familiar with quantum mechanics.

Nonequilibrium Quantum Field Theory
  • Esteban A. Calzetta, Bei-Lok B. Hu
  • Published online:
    23 October 2009
    Print publication:
    24 July 2008
  • Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics.

Quantum Geometry
  • A Statistical Field Theory Approach
  • Jan Ambjørn, Bergfinnur Durhuus, Thordur Jonsson
  • Published online:
    20 October 2009
    Print publication:
    19 June 1997
  • 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. With chapters on random walks, random surfaces, two- and higher dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach uses discrete approximations and develops analytical and numerical tools. Continuum physics is recovered through scaling limits at phase transition points and the relation to conformal quantum field theories coupled to quantum gravity is described. The most important numerical work is covered, but the main aim is to develop mathematically precise results that have wide applications. Many diagrams and references are included.

Kinetic Theory in the Expanding Universe
  • Jeremy Bernstein
  • Published online:
    20 October 2009
    Print publication:
    26 August 1988
  • This graduate/research level text is a self-contained exposition of the applications of kinetic theory to basic problems in modern cosmology, such as the role of stable and unstable massive neutrinos and the theory of cosmological helium production. There has been rapid development of the theory of the origin and evolution of the universe in recent years, stimulated in large part by new observations and theories in astrophysics and particle physics. This book takes a different approach and studies what can be concluded from the application to cosmological problems of kinetic theory and, in particular, the Boltzmann equation and its solutions. The book begins with a brief survey of the necessary relativity, cosmodynamics, and kinetic theory, before going on to discuss specific problems, such as the role of stable and unstable massive neutrinos, electron-poritron annihilation, and the theory of cosmological helium production. The focus is in obtaining both theoretical understanding and concrete numerical results.

Twistor Geometry and Field Theory
  • R. S. Ward, Raymond O. Wells, Jr
  • Published online:
    08 October 2009
    Print publication:
    15 February 1990
  • This book deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, algebraic topology and results in a new perspective on the properties of space and time. The authors firstly develop the mathematical background, then go on to discuss Yang-Mills fields and gravitational fields in classical language, and in the final part a number of field-theoretic problems are solved. Issued here for the first time in paperback, this self-contained volume should be of use to graduate mathematicians and physicists and research workers in theoretical physics, relativity, and cosmology.

The Interacting Boson-Fermion Model
  • F. Iachello, P. van Isacker
  • Published online:
    07 October 2009
    Print publication:
    30 August 1991
  • The interacting boson-fermion model has become in recent years the standard model for the description of atomic nuclei with an odd number of protons and/or neutrons. This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. The book addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed. The book is the first comprehensive treatment of the subject and will appeal to both theoretical and experimental physicists. The large number of explicit formulas for level energies, electromagnetic transition rates and intensities of transfer reactions presented in the book provide a simple but detailed way to analyse experimental data. This book can also be used as a textbook for advanced graduate students.

Loops, Knots, Gauge Theories and Quantum Gravity
  • Rodolfo Gambini, Jorge Pullin
  • Foreword by Abhay Ashtekar
  • Published online:
    29 September 2009
    Print publication:
    13 November 1996
  • Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed in detail. Following chapters move on to consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.

Page 5 of 6