The Global Approach to Quantum Field Theory / Edition 2

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This new volume takes a complete look at how classical field theory, quantum mechanics and quantum field theory are interrelated. It takes a global approach and discusses the importance of quantization by relating it to different theories such as tree amplitude and conservation laws. There are special chapters devoted to Euclideanization and renormalization, space and time inversion and the closed-time-path formalism.

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Product Details

Table of Contents

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. Asymptotic 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
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 Index
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 *lq[4 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 Appendix A: Superanalysis Appendix B: The Structure Functions to All Orders Appendix C: The Case in Which OC is not Supersymmetric Appendix D: Properties of Vilkovisky's Connection Appendix E: Analytic Continuation in Dimension Appendix F: Conformally Flat Spacetimes Index

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