The Global Approach to Quantum Field Theory

Hardcover | February 15, 2003

byBryce DeWitt

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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 studiedin 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 isconstructed 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, areincluded at the end.

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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 Hamil...

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

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Format:HardcoverDimensions:1130 pages, 9.45 × 6.61 × 2.68 inPublished:February 15, 2003Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198510934

ISBN - 13:9780198510932

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Table of Contents

Classical Dynamical Theory1. Fundamentals2. Dynamics and invariance transformations3. Small disturbances and Green's functions4. The Peierls bracket5. Finite disturbances. Tree theorems. Asymptotic fields.6. Conservation lawsThe Heuristic Road to Quantization. The Quantum Formalism and Its Interpretation7. Classical theory of measurement8. Quantum theory of measurement9. Interpretation of the quantum formalism I10. The Schwinger variational principle11. The quantum mechanics of standard canonical systems12. Interpretation of the quantum formalism IIEvaluation and Approximation of Feynman Functional Integrals13. The functional integral for standard canonical systems14. Approximation and evaluation of the path integral15. The nonrelativistic particle in a curved space16. The heat kernelLinear Systems17. Linear boson fields in stationary backgrounds18. Quantization of linear boson fields19. Linear fermion fields. Stationary backgrounds.20. Quantization of linear fermion fields21. Linear fields in nonstationary backgrounds22. Linear (or linearized) fields possessing invariant flowsNonlinear Fields23. The effective action, the S-matrix, and Slavnov-Taylor identities24. 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 kernel28. Vacuum currents. Anomalies.29. More vacuum phenomena30. Black hole vacua. Hawking radiation.31. The closed-time-path or 'in-in' formalismSpecial Topics32. Euclideanization and Renormalization33. Canonical transformations. Space inversion and time reversal.34. Quantum electrodynamics35. The Yang-Mills and gravitational fieldsSimple Illustrative ExamplesX0. The nonrelativistic particle in flat spaceX1. A simple Fermi systemX2. A Fermi doubletX3. Fermi multipletX4. The Fermi oscillatorX5. The Bose oscillatorX6. A fourth-order systemX7. A model for ghostsX8. Free scalar field in flat spacetimeX9. Massive vector field in four dimensional flat spacetimeX10. Massive antisymmetric tensor fieldX11. Massive symmetric tensor field in flat spacetimeX12. Massive spinor field in flat spacetimeX13. Massive spin-3/2 field in flat spacetimeX14. Elecromagnetic field in flat spacetimeX15. Massless symmetric tensor field in flat spacetimeX16. Massless spinor field in four dimensional flat spacetimeX17. Massless spin-3/2 field in four dimensional flat spacetimeX18. Renormalization group and spontaneous symmetry breaking in the (lambda phi) to the fourth power modelX19. The relativistic particle in Minkowski spacetimeX20. A simple soluble nonlinear modelX21. Quantum mechanics on a circleX22. Quantum mechanics on a Klein bottleX23. Ghosts for ghostsX24. Massive antisymmetric tensor fieldA. Appendix AB. Appendix BC. Appendix CD. Appendix DE. Appendix EF. Appendix F

Editorial Reviews

`... of significant interest to researchers in quantum field theory and quantum gravity, particularly in the general relativity community.'R. Wald, University of Chicago