The Global Approach to Quantum Field Theory

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9780198712855: The Global Approach to Quantum Field Theory

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.

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Recensione:

... 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)

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. ( Luis Alvarez-Gaume, 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)

Over the past five decades, DeWitt has worked on the gamut of formal ideas in QFT. 'The Global Approach to Quantum Field Theory' crystallizes a pioneer's view of the subject's development during those years. ( Stanley Deser, Physics Today, March 2004)

Contenuti:

  • I: Classical Dynamical Theory
  • 1: Fundamentals
  • 2: Dynamics and Invariance Transformations
  • 3: Small Disturbances and Green's Functions
  • 4: The Peierls Bracket
  • 5: Finite Disturbances. Tree Theorems. Asmptotic Fields
  • 6: Conservation Laws
  • II: The Heuristic Road to Quantization. The Quantum Formalism and its Interpretation
  • 7: Classical Theory of Measurement
  • 8: Quantum Theory of Measurement
  • 9: Interpretation of the Quantum Formalism I
  • 10: The Schwinger Variational Principle and the Feynman Functional Integral
  • 11: The Quantum Mechanics of Standard Canonical Systems
  • 12: Interpretation of the Quantum Formalism II
  • III: Evaluation and Approximation of Feynman Functional Integrals
  • 13: 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
  • IV: Linear Systems
  • 17: 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
  • V: Nonlinear Fields
  • 23: 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
  • VI: Tools for Quantum Field Theory. Applications
  • 27: 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
  • VII: Special Topics
  • 32: Euclideanization and Renormalization
  • 33: Canonical Transformations. Space Inversion and Time Reversal
  • 34: Quantum Electrodynamics
  • 35: The Yang-Mills and Gravitational Fields
  • VIII: Examples. Simple Exercises in the use of the Global Formalism
  • X0: 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: Electromagnetic 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: Massless Antisymmetric Tensor Field

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Bryce S. DeWitt
Editore: Oxford University Press, United Kingdom (2014)
ISBN 10: 0198712855 ISBN 13: 9780198712855
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Descrizione libro Oxford University Press, United Kingdom, 2014. Multiple copy pack. Condizione libro: New. 240 x 170 mm. Language: English . Brand New Book. 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. Codice libro della libreria AOP9780198712855

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Bryce S. DeWitt
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ISBN 10: 0198712855 ISBN 13: 9780198712855
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Descrizione libro Oxford University Press, United Kingdom, 2014. Multiple copy pack. Condizione libro: New. 240 x 170 mm. Language: English . Brand New Book. 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. Codice libro della libreria AOP9780198712855

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Descrizione libro Oxford Univ Pr, 2014. Paperback. Condizione libro: Brand New. 1136 pages. 9.25x6.50x2.50 inches. In Stock. Codice libro della libreria __0198712855

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Descrizione libro 2014. Paperback. Condizione libro: New. 241mm x 169mm x. Paperback. 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 br.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 1136 pages. 1.864. Codice libro della libreria 9780198712855

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