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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 3 of 6

Superstring Theory
  • 25th Anniversary Edition
  • Volume 2, Loop Amplitudes, Anomalies and Phenomenology
  • Michael B. Green, John H. Schwarz, Edward Witten
  • Published online:
    05 September 2012
    Print publication:
    26 July 2012
  • Twenty-five years ago, Michael Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. Volume 2 is concerned with the evaluation of one-loop amplitudes, the study of anomalies and phenomenology. It examines the low energy effective field theory analysis of anomalies, the emergence of the gauge groups E8 x E8 and SO(32) and the four-dimensional physics that arises by compactification of six extra dimensions. Featuring a new Preface setting the work in context in light of recent advances, this book is invaluable for graduate students and researchers in high energy physics and astrophysics, as well as mathematicians.

Superstring Theory
  • 25th Anniversary Edition
  • Volume 1, Introduction
  • Michael B. Green, John H. Schwarz, Edward Witten
  • Published online:
    05 September 2012
    Print publication:
    26 July 2012
  • Twenty-five years ago, Michael Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. A self-contained introduction to superstrings, Volume 1 begins with an elementary treatment of the bosonic string, before describing the incorporation of additional degrees of freedom: fermionic degrees of freedom leading to supersymmetry and internal quantum numbers leading to gauge interactions. A detailed discussion of the evaluation of tree-approximation scattering amplitudes is also given. Featuring a new preface setting the work in context in light of recent advances, this book is invaluable for graduate students and researchers in general relativity and elementary particle theory.

Classical Solutions in Quantum Field Theory
  • Solitons and Instantons in High Energy Physics
  • Erick J. Weinberg
  • Published online:
    05 September 2012
    Print publication:
    16 August 2012
  • Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions.

Statistical Field Theory
  • Volume 2, Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems
  • Claude Itzykson, Jean-Michel Drouffe
  • Published online:
    05 August 2012
    Print publication:
    29 September 1989
  • Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. 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. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.

Statistical Field Theory
  • Volume 1, From Brownian Motion to Renormalization and Lattice Gauge Theory
  • Claude Itzykson, Jean-Michel Drouffe
  • Published online:
    05 August 2012
    Print publication:
    29 September 1989
  • Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. 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. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.

Quantum Fields in Curved Space
  • N. D. Birrell, P. C. W. Davies
  • Published online:
    05 August 2012
    Print publication:
    25 February 1982
  • 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.

The Interacting Boson Model
  • F. Iachello, A. Arima
  • Published online:
    05 November 2011
    Print publication:
    20 August 1987
  • 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. In particular, this book presents the mathematical techniques used to analyze the structure of the model. It also collects in a single, easily accessible reference all the formulas that have been developed throughout the years to account for collective properties of nuclei. Suitable for both theorists and experimentalists.

An Introduction to Regge Theory and High Energy Physics
  • P. D. B. Collins
  • Published online:
    07 October 2011
    Print publication:
    28 April 1977
  • Originally published in 1977, this book presents an extended introduction to the theory of hadrons, the elementary particles which occur in the atomic nucleus. The main emphasis is on the theory of the complex angular momentum plane 'Regge theory', which has grown from Regge's demonstration in 1959 that it is useful to regard angular momentum as a complex variable when discussing solutions of the Schrodinger equation for non-relativistic potential scattering. This theory helps to classify the many different particles which have been discovered in recent years, to explain the forces between these particles and to predict the results of high-energy scattering experiments. Regge theory thus serves as a unifying concept drawing together many different features of high-energy physics. This monograph is intended primarily for research students just beginning to concern themselves with particle physics, but more experienced workers will also find much to interest them in this detailed survey of the basic ideas and results of Regge theory.

Hamiltonian Mechanics of Gauge Systems
  • Lev V. Prokhorov, Sergei V. Shabanov
  • Published online:
    07 October 2011
    Print publication:
    22 September 2011
  • The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Gravitational Physics of Stellar and Galactic Systems
  • William C. Saslaw
  • Published online:
    05 July 2011
    Print publication:
    25 July 1985
  • 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. In a rapidly developing area of astronomy, it is the first comprehensive treatise on the subject to be published since the early 1960s. Concentrating on the basic physics, at a graduate student level, it also develops many astronomical applications in considerable detail. The book is self-contained. Most results are derived from preceding ones in a straightforward way. It is written to bring out the physical content behind the mathematical formulae, and contains a number of exercises and suggestions for research topics. Bibliographies with nearly 300 selected references provide gateways into the literature.

Hamiltonian Systems
  • Chaos and Quantization
  • Alfredo M. Ozorio de Almeida
  • Published online:
    05 July 2011
    Print publication:
    24 February 1989
  • This introduction to the theory of Hamiltonian chaos outlines the main results in the field, and goes on to consider implications for quantum mechanics. The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and most productive areas in physics and applied mathematics. In its first six chapters, this timely book introduces the theory of classical Hamiltonian systems. The aim is not to be comprehensive but, rather, to provide a mathematical trunk from which the reader will be able to branch out. The main focus is on periodic orbits and their neighbourhood, as this approach is especially suitable as an introduction to the implications of the theory of chaos in quantum mechanics, which are discussed in the last three chapters.

Functional Integrals and Collective Excitations
  • Victor Nikolaevich Popov
  • Published online:
    01 June 2011
    Print publication:
    07 January 1988
  • This book describes the theory and selected applications of one of the most important mathematical tools used in the theoretical investigation of collective excitations in statistical physics, such as occur in superfluidity, superconductivity, plasma dynamics, superradiation, and in phase transitions. The author, who is a distinguished physicist and leading researcher in this area, begins with an introduction to functional integral techniques in equilibrium statistical thermodynamics, and discusses the expression of partition functions and Green functions in terms of functional integrals. Subsequent sections deal with the application of functional integrals in superfluid Bose systems, systems with Coulomb interaction, and superfluid Fermi systems. The final section considers the application of the concept of Bose-condensation of auxiliary fields to the theory of crystals, heavy atoms and also to the theory of model Hamiltonians (BCS and Dicke models).

Supermanifolds
  • 2nd edition
  • Bryce DeWitt
  • Published online:
    01 June 2011
    Print publication:
    28 May 1992
  • This is an updated and expanded second edition of a successful and well-reviewed text presenting a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassman variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of super-analogs of Lie derivatives, connections, metric, curvature, geodesics, Killing flows, conformal groups, etc. The book goes on to discuss the theory of super Lie groups, super Lie algebras, and invariant geometrical structures on coset spaces. Complete descriptions are given of all the simple super Lie groups. The book then turns to applications. Chapter 5 contains an account of the Peierals bracket for superclassical dynamical systems, super Hilbert spaces, path integration for fermionic quantum systems, and simple models of Bose–Fermi supersymmetry. The sixth and final chapter, which is new in this revised edition, examines dynamical systems for which the topology of the configuration supermanifold is important. A concise but complete account is given of the pathintegral derivation of the Chern–Gauss–Bonnet formula for the Euler–Poincaré characteristic of an ordinary manifold, which is based on a simple extension of a point particle moving freely in this manifold to a supersymmetric dynamical system moving in an associated supermanifold. Many exercises are included to complement the text.

Introduction to Supersymmetry
  • Peter G. O. Freund
  • Published online:
    01 June 2011
    Print publication:
    13 November 1986
  • 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. It is the aim of this book to provide a brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The book starts with a physical motivation of supersymmetry, a presentation of the mathematics of Lie superalgebras, supergroups and superspace. Techniques for constructing manifestly globally supersymmetric field theories are given, using the superfield formalism. To allow for a clear flow of ideas, the basic ideas and techniques are worked out in low space dimensionalities where the formulae do not obscure the concepts. Generalizations to four space-time dimensions are then readily come by. Some quantum aspects are discussed. Possible phenomenological applications are not emphasized. Supergravities, locally supersymmetric theories are then considered in 4 and 11 dimensions, in component formalism. An introduction to supersymmetry will be of interest to postgraduate students and researchers in theoretical and particle physics, especially those working in quantum field theory, quantum gravity, general relativity and supergravity. The book will also be of interest to mathematicians with an interest in theoretical physics.

Classical Measurements in Curved Space-Times
  • Fernando de Felice, Donato Bini
  • Published online:
    03 May 2011
    Print publication:
    29 July 2010
  • 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.

The Structure of the Proton
  • Deep Inelastic Scattering
  • R. G. Roberts
  • Published online:
    03 May 2011
    Print publication:
    30 November 1990
  • This graduate/research level book describes our 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 which bind the quarks together are described in terms of the modern theory of quantum chromodynamics (QCD), the 'glue' binding the quarks being mediated by new constituents called gluons. Larger and new particle accelerators probe the interactions between quarks and gluons at shorter distances. The understanding of this detailed substructure and of the fundamental forces responsible is one of the keys to unravelling the physics of the structure of matter. This book will be of interest to all theoretical and experimental particle physicists.

Group Structure of Gauge Theories
  • L. O'Raifeartaigh
  • Published online:
    04 April 2011
    Print publication:
    13 March 1986
  • This monograph provides an account of the structure of gauge theories from a group theoretical point of view. The first part of the text is devoted to a review of those aspects of compact Lie groups (the Lie algebras, the representation theory, and the global structure) which are necessary for the application of group theory to the physics of particles and fields. The second part describes the way in which compact Lie groups are used to construct gauge theories. Models that describe the known fundamental interactions and the proposed unification of these interactions (grand unified theories) are considered in some detail. The book concludes with an up to date description of the group structure of spontaneous symmetry breakdown, which plays a vital role in these interactions. This book will be of interest to graduate students and to researchers in theoretical physics and applied mathematics, especially those interested in the applications of differential geometry and group theory in physics.

Differential Geometry, Gauge Theories, and Gravity
  • M. Göckeler, T. Schücker
  • Published online:
    04 April 2011
    Print publication:
    25 December 1987
  • Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Path Integral Methods in Quantum Field Theory
  • R. J. Rivers
  • Published online:
    04 April 2011
    Print publication:
    12 November 1987
  • This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researchers in theoretical physics, especially those with an interest in experimental and theoretical particle physics and quantum field theory.

String Theory
  • Volume 1, An Introduction to the Bosonic String
  • Joseph Polchinski
  • Published online:
    29 March 2011
    Print publication:
    13 October 1998
  • String Theory comprises two volumes which give a comprehensive and pedagogic account of the subject. Volume 1, first published in 1998, provides a thorough introduction to the bosonic string. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of their finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is included. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.

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