The Global Approach to Quantum Field Theory
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The Global Approach to Quantum Field Theory: (114 International Series of Monographs on Physics)

The Global Approach to Quantum Field Theory: (114 International Series of Monographs on Physics)


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About the Book

The book shows how classical field theory, quantum mechanics, and quantum field theory are related. Thedescription 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 toEuclideanization 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.

Table of Contents:
Classical Dynamical Theory1: Fundamentals 2: Dynamics and invariance transformations 3: Small disturbances and Green's functions 4: The Peierls bracket 5: Finite disturbances. Tree theorems. Asymptotic fields. 6: Conservation laws The Heuristic Road to Quantization. The Quantum Formalism and Its Interpretation7: Classical theory of measurement 8: Quantum theory of measurement 9: Interpretation of the quantum formalism I 10: The Schwinger variational principle 11: The quantum mechanics of standard canonical systems 12: Interpretation of the quantum formalism II Evaluation and Approximation of Feynman Functional Integrals13: The functional integral for standard canonical systems 14: Approximation and evaluation of the path integral 15: The nonrelativistic particle in a curved space 16: The heat kernel Linear Systems17: Linear boson fields in stationary backgrounds 18: Quantization of linear boson fields 19: Linear fermion fields. Stationary backgrounds. 20: Quantization of linear fermion fields 21: Linear fields in nonstationary backgrounds 22: Linear (or linearized) fields possessing invariant flows Nonlinear Fields23: The effective action, the S-matrix, and Slavnov-Taylor identities 24: Gauge theories I. General formalism. 25: Gauge theories II. Background Field Methods. Scattering Theory. 26: Case-I gauge theory without ghosts. Description of cases II and III. Tools for Quantum Field Theory. Applications27: The heat kernel 28: Vacuum currents. Anomalies. 29: More vacuum phenomena 30: Black hole vacua. Hawking radiation. 31: The closed-time-path or 'in-in' formalism Special Topics32: Euclideanization and Renormalization 33: Canonical transformations. Space inversion and time reversal. 34: Quantum electrodynamics 35: The Yang-Mills and gravitational fields Simple Illustrative ExamplesX0: The nonrelativistic particle in flat space X1: A simple Fermi system X2: A Fermi doublet X3: Fermi multiplet X4: The Fermi oscillator X5: The Bose oscillator X6: A fourth-order system X7: A model for ghosts X8: Free scalar field in flat spacetime X9: Massive vector field in four dimensional flat spacetime X10: Massive antisymmetric tensor field X11: Massive symmetric tensor field in flat spacetime X12: Massive spinor field in flat spacetime X13: Massive spin-3/2 field in flat spacetime X14: Elecromagnetic field in flat spacetime X15: Massless symmetric tensor field in flat spacetime X16: Massless spinor field in four dimensional flat spacetime X17: Massless spin-3/2 field in four dimensional flat spacetime X18: Renormalization group and spontaneous symmetry breaking in the (lambda phi) to the fourth power model X19: The relativistic particle in Minkowski spacetime X20: A simple soluble nonlinear model X21: Quantum mechanics on a circle X22: Quantum mechanics on a Klein bottle X23: Ghosts for ghosts X24: Massive antisymmetric tensor field A: Appendix A B: Appendix B C: Appendix C D: Appendix D E: Appendix E F: Appendix F

About the Author :
Prof. Bryce DeWitt 2411 Vista Lane Austin, Texas 78703 dewitt@physics.utexas.edu tel: 001-512-478-6037 fax: 001-512-471-0890 Birthplace: Dinuba, California, 8 January 1923

Review :
`... a legacy the author is leaving to those interested in understanding quantum field theory at the deepest level.' G. Veneziano, CERN, Geneva `... of significant interest to researchers in quantum field theory and quantum gravity, particularly in the general relativity community.' R. Wald, University of Chicago


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Product Details
  • ISBN-13: 9780198510932
  • Publisher: Oxford University Press
  • Publisher Imprint: Oxford University Press
  • Height: 257 mm
  • No of Pages: 1136
  • Spine Width: 68 mm
  • Width: 180 mm
  • ISBN-10: 0198510934
  • Publisher Date: 06 Mar 2003
  • Binding: SA
  • Language: English
  • Series Title: 114 International Series of Monographs on Physics
  • Weight: 2744 gr


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