ボゴリューボフ、シルコフ著
『量子場の理論(場の量子論)入門』第三版
N.N. Bogoliubov, D.V. Shirkov
『INTRODUCTION TO THE THEORY OF QUANTIZED FIELDS』 3rd EDITION
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ボゴリューボフ変換で有名なボゴリューボフと
繰り込み群の手法開発への貢献で有名なシルコフによる量子場の理論の教科書です。
CHAPTER 1. CLASSICAL THEORY OF FREE FIELDS
§ 1. Lagrangian Formalism
§ 2. Noether's Theorem and Dynamic Invariants
§ 3. Scalar Field
§ 4. The Vector Field
§ 5. The Electromagnetic Field
§ 6. The Spinor Field. Dirac Matrices and Transformation Laws for Spinor Functions
§ 7. The Spinor Field. Properties of the Solutions and Dynamic Variables
§ 8. Lagrangian of a System of Fields
CHAPTER 2. QUANTUM THEORY OF FREE FIELDS
§ 9. General Principles of Quantization of Wave Fields
§10. Setting Up the Commutation Relations
§11. Scalar and Vector Fields
§12. The Electromagnetic Field
§13. The Spinor Field
§14. CPT Theorem
CHAPTER 3. SINGULAR FUNCTIONS AND REGULARIZATION
§15. Green's Functions
§16. Properties of Green's Functions and Regularization
§17. Reduction to Normal Form
§18. Coefficient Functions
CHAPTER 4. SCATTERING MATRIX
§19. Multiplication of Operator Functions
§20. Basic Concepts of the Theory of Interacting Fields
§21. The Interaction Lagrangian and the S-Matrix
§22. Evaluation of Chronological Products
§23. Reduction of the S-Matrix to the Normal Form
§24. Feynman's Rules for the Evaluation of Matrix Elements of the Scattering Matrix
§25. Probabilities of Scattering Processes and Effective Cross Sections
§26. Examples of Calculation of Second-Order Processes
CHAPTER 5. REMOVAL OF DIVERGENCES FROM THE S-MATRIX
§27. On the Divergences of the S-Matrix in Electrodynamics (Second Order)
§28. Divergences of the s-Matrix Electrodynamics (Third Order)
$29. General Rules for the Removal of Divergences from the S-Matrix
§30. Structure of the R-Operation
§31. Analytic Properties of the Coefficient Functions in the Momentum Representation
§32. Classification of the Renormalizability of Different Theories
CHAPTER 6. APPLICATIONS OF THE GENERAL THEORY OF REMOVAL OF DIVERGENCES
§33. Spinor Electrodynamics. I. General Form of Counter Terms
§34. Spinor Electrodynamics. Il. Mass and Charge Renormalization
§35. Spinor Electrodynamics. III. Radiative Corrections of the Second Order
§36. Some Models of Strong Interactions
§37. Complete Green's Functions and Vertex Functions
§38. Schwinger and Dyson Equations
CHAPTER 7. SCHROEDINGER EQUATIONS AND DYNAMIC VARIABLES
$39. Schroedinger Equation for the State Amplitude
§40. Dynamic Variables of a System of Interacting Fields
§41. Vacuum Polarization and the Anomalous Magnetic Moment of the Electron
§42. Dirac Equation with Radiative Corrections
§43. Functional Integrals in Quantum Field Theory
§44. Generating Functionals and Green's Functions
§45. Gauge Transformations in Spinor Electrodynamics
§46. Investigation of the Bloch-Nordsieck Model
CHAPTER 9. THE RENORMALIZATION GROUP
§47. The Group of Multiplicative Renormalizations in Quantum Field Theory
§48. General Analysis of Group Equations.
$49. Asymptotic Analysis in the Ultraviolet Region
$50. Analysis of Green’s Function in Spinor Electrodynamics
§51. Strong-Interaction Models
CHAPTER 10. DISPERSION RELATIONS
§52. Basic Properties of the S-Matrix in Local Field Theory
§53. Spectral Representation of the Pion Green's Function
§54. Spectral Representation of the Fermion Green's Function
§55. The Jost-Lehmann-Dyson Representation
§56. Derivation of Dispersion Relations for Pion-Nucleon Scattering
§57. Dispersion Relations for Pion-Nucleon Forward Scattering
APPENDIX I. ELEMENTS OF ISOSPIN FORMALISM APPENDIX II, LIST OF SINGULAR FUNCTIONS
APPENDIX III. LIST OF FORMULAS FOR THE EVALUATION OF MATRIX ELEMENTS
INDEX
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