Kirjahaku

Bryce DeWitt, a student of Nobel Laureate Julian Schwinger, was himself one of the towering figures in 20th century physics, particularly renowned for his seminal contributions to quantum field theory, numerical relativity and quantum gravity. In late 1971 DeWitt gave a course on gravitation at Stanford University, leaving almost 400 pages of detailed handwritten notes. Written with clarity and authority, and edited by his former student Steven Christensen, these timeless lecture notes, containing material or expositions not found in any other textbooks, are a gem to be discovered or re-discovered by anyone seriously interested in the study of gravitational physics.

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.

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.

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.