Bücher der Reihe Cambridge Monographs on Mathematical Physics

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 by digital technology, enabling Cambridge to keep the book in print for specialists and students when other traditional methods of printing would have been infeasible.

This book will be of great interest to graduate students wishing to learn about semi-classical methods in nuclear physics.

This study deals with the twistor treatment of linear and non-linear partial differential equations. The authors develop the mathematical background, go on to discuss Yang Mills fields and gravitational fields in classical language and finish by solving a number of field-theoretic problems.

Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, like tensors, algebras, Fock spaces, and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in departments of mathematics and physics.

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.

This book introduces the lattice approach to quantum field theory. The spectacular successes of this technique include compelling evidence that exchange of gauge gluons can confine the quarks within subnuclear matter. The lattice framework enables novel schemes for quantitative calculation and has caused considerable cross-disciplinary activity between elementary particle and solid state physicists. The treatment begins with the lattice definition of a path integral and ends on Monte Carlo simulation methods. Other topics include invariant group integration, duality, mean field theory and renormalization group techniques. The reader is assumed to have a basic background in relativistic quantum mechanics and some exposure to gauge theories.

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-Poincare 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.

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.

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.

The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.

This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role.

Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity and provides a detailed description of mathematical methods. It is ideal for theoretical physicists, researchers and Ph.D. students.

This overview of mass dimension one fermions and the eigenspinors of the charge conjugation operator is written by one of the theoretical physicists involved in their discovery. With mass dimension one fermions being candidates for dark matter, this is an important book for students and researchers in quantum field theory.

A self-contained and unique text systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity.

Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on this area of research.

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.

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. It discusses the most important classes of solitons: kinks, vortices and magnetic monopoles, as well as Euclidean solutions.

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.

The development of gauge theories has provided the basis for a complete and consistent account of weak interactions - for example between neutrinos and matter - whilst displaying their unity with electromagnetism. This 1979 book examines gauge theories, which were first proposed in this context in 1976.

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.

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments. 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.

Now in paperback, this book is the first comprehensive and coherent introduction to the role of cosmic strings and other topological defects in the universe. Ample introductory material makes the book accessible to the wide audience of particle physicists, astrophysicists and cosmologists for whom this topic is of immediate interest.

This book provides a complete treatise of the canonical quantisation of general relativity and the loop quantum gravity theory. Mathematical concepts are provided, so it can be read by graduate students with a basic knowledge of quantum field theory or general relativity.

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, not only those of interest to particle physics. It will interest graduate students and researchers in theoretical physics who are familiar with quantum mechanics.

Investigating the issues involved in gravitational collapse, this book includes a detailed review of recent research into the subject, and several examples of collapse models are investigated in detail. It will be of interest to graduate students and academic researchers in gravitation physics, fundamental physics, astrophysics, and cosmology.

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.

In this text, Cartier and DeWitt-Morette, using their complementary interests and expertise, successfully condense and apply the essentials of Functional Integration to a great variety of systems, showing this mathematically elusive technique to be a robust, user friendly and multipurpose tool.