The Global Approach to Quantum Field Theory - Couverture rigide

DeWitt, Bryce

Couverture rigide

ISBN 10 : 0198510934 ISBN 13 : 9780198510932

Editeur : Clarendon Press, 2003

Synopsis

The Global Approach to Quantum Field Theory Covers classical field theory, quantum mechanics and the major theoretical aspects of quantum field theory, and shows how they are related. Here, fields are viewed as global entities in spacetime rather than as systems evolving from one instant of time to the next. Full description

A propos du livre

Présentation de l'éditeur :

The book shows how classical field theory, quantum mechanics, and quantum field theory are related. The description is global from the outset. Quantization is explained using the Peierls bracket rather than the Poisson bracket. This allows one to deal immediately with observables, bypassing the canonical formalism of constrained Hamiltonian systems and bigger-than-physical Hilbert (or Fock) spaces. The Peierls bracket leads directly to the Schwinger variational principle and the Feynman functional integral, the latter of which is taken as defining the quantum theory. Also included are the theory of tree amplitudes and conservation laws, which are presented classically and later extended to the quantum level. The quantum theory is developed from the many-worlds viewpoint, and ordinary path integrals and the topological issues to which they give rise are studied in some detail. The theory of mode functions and Bogoliubov coefficients for linear fields is fully developed, and then the quantum theory of nonlinear fields is confronted. The effective action, correlation functions and counter terms all make their appearance at this point, and the S-matrix is constructed via the introduction of asymptotic fields and the LSZ theorem. Gauge theories and ghosts are studied in great detail. Many applications of the formalism are given: vacuum currents, anomalies, black holes, fourth-order systems, higher spin fields, the (lambda phi) to the fourth power model (and spontaneous symmetry breaking), quantum electrodynamics, the Yang-Mills field and its topology, the gravitational field, etc. Special chapters are devoted to Euclideanization and renormalization, space and time inversion, and the closed-time-path or ``in-in'' formalism. Emphasis is given throughout to the role of the functional-integral measure in the theory. Six helpful appendices, ranging from superanalysis to analytic continuation in dimension, are included at the end.

Revue de presse :

The book's presentation is very impressive. Conceptual problems are elegantly exhibited and there is an inner coherent logic of exposition that could only come from someone who had long and deeply reflected on the subject, and made important contributions to it. (CERN Courier)

This book is one of the best books dealing with quantum field theory existing today. It will be of great interest for graduate and postgraduate students as well as workers in the domains of quantum field theory in flat and in curved spacetime and string theories ... share the deep and unique vision of the quantum theory of fields and its formalism by one of its greatest expositors. (Journal of Physics)

... should be particularly useful for quantum field theorists (especially students), theoretical physicists and mathematicians with an interest in physics. (CERN Courier)

À propos de cette édition

• Éditeur: Clarendon Press
• Date d'édition: 2003
• ISBN 10: 0198510934
• ISBN 13: 9780198510932
• Reliure: Relié
• Nombre de pages: 1136