Quantum field theory

Quantum Field Theory
Half-Title
International Series In Pure And Applied Physics
Title-Page
Copyright
Contents
Preface To The Dover Edition
Preface
General References
Chapter One Classical Theory
	1-1 Principle Of Least Action
		1-1-1 Classical Motion
		1-1-2 Electromagnetic Field As An Infinite Dynamical System
		1-1-3 Electromagnetic Interaction Of A Point Particle
	1-2 Symmetries And Conservation Laws
		1-2-1 Fundamental Invariants
		1-2-2 Energy Momentum Tensor
		1-2-3 Internal Symmetries
	1-3 Propagation And Radiation
		1-3-1 Green Functions
		1-3-2 Radiation
	Notes
Chapter Two The Dirac Equation
	2-1 Toward A Relativistic Wave Equation
		2-1-1 Quantum Mechanics And Relativity
		2-1-2 The Dirac Equation
		2-1-3 Relativistic Covariance
	2-2 Physical Content
		2-2-1 Plane Wave Solutions And Projectors
		2-2-2 Wave Packets
		2-2-3 Electromagnetic Coupling
		2-2-4 The Foldy-Wouthuysen Transformation
	2-3 Hydrogen-Like Atoms
		2-3-1 Nonrelativistic Versus Relativistic Spectrum
		2-3-2 Dirac Theory
			Hyperfine Structure
			Radiative Corrections
			Nuclear Effects
			Two-Body Relativistic Corrections
	2-4 Hole Theory And Charge Conjugation
		2-4-1 Reinterpretation Of Negative Energy Solutions
		2-4-2 Charge Conjugation
		2-4-3 Zero-Mass Particles
	2-5 Dirac Propagator
		2-5-1 Free Propagator
		2-5-2 Propagation In An Arbitrary External Electromagnetic Field
		2-5-3 Application To The Coulomb Scattering
		2-5-4 Fock-Schwinger Proper Time Method
	Notes
Chapter Three Quantization Free Fields
	3-1 Canonical Quantization
		3-1-1 General Formulation
		3-1-2 Scalar Field
		3-1-3 Charged Scalar Field
		3-1-4 Time-Ordered Product
		3-1-5 Thermodynamic Equilibrium
	3-2 Quantized Radiation Field
		3-2-1 Indefinite Metric
		3-2-2 Propagator
		3-2-3 Massive Vector Field
		3-2-4 Vacuum Fluctuations
	3-3 Dirac Field And Exclusion Principle
		3-3-1 Anticommutators
		3-3-2 Fock Space For Fermions
		3-3-3 relation Between Spin And Statistics-Propagator
	3-4 Discrete Symmetries
		3-4-1 Parity
		3-4-2 Charge Conjugation
		3-4-3 Time Reversal
		3-4-4 Summary
	Notes
Chapter Four Interaction With An External Field
	4-1 Quantized Electromagnetic Field Interacting With A Classical Source
		4-1-1 Emission Probabilities
		4-1-2 Emitted Energy And The Infrared Catastrophe
		4-1-3 Induced Absorption And Emission
		4-1-4 S-Matrix And Evolution Operator
	4-2 Wick\'s Theorem
		4-2-1 Bose Fields
		4-2-2 Fermi Fields
		4-2-3 General case
	4-3 Quantized Dirac Field Interacting With A Classical Potential
		4-3-1 General Formalism
		4-3-2 Emission Rate To Lowest Order
		4-3-3 Pair Creation In A Constant Uniform Electric Field
		4-3-4 The Euler-Heisenberg Effective Lagrangian
	Notes
Chapter Five Elementary Processes
	5-1 S-Matrix And Asymptotic Theory
		5-1-1 Cross Sections
		5-1-2 Asymptotic Theory
		5-1-3 Reduction Formulas
		5-1-4 Generating Functional
		5-1-5 Connected Parts
		5-1-6 Fermions
		5-1-7 Photons
	5-2 Applications
		5-2-1 Compton Effect
		5-2-2 Pair Annihilation
		5-2-3 Positronium Lifetime
		5-2-4 Bremsstrahlung
	5-3 Unitarity And Causality
		5-3-1 Unitarity And Partial Wave Decomposition
		5-3-2 Causality And Analyticity
		5-3-3 The Jost-Lehmann-Dyson Representation
		5-3-4 Forward Dispersion Relations
		5-3-5 Momentum Transfer Analyticity
	Notes
Chapter Six Perturbation Theory
	6-1 Interaction Representation And Feynman Rules
		6-1-1 Self-Interacting Scalar Field
		6-1-2 Feynman Rules For Spinor Electrodynamics
		6-1-3 Electron-Electron And Electron-Positron Scattering
		6-1-4 Scalar Electrodynamics
	6-2 Diagrammatics
		6-2-1 Loopwise Expansion
		6-2-2 Truncated And Proper Diagrams
		6-2-3 Parametric Representation
		6-2-4 Euclidean Green Functions
	6-3 Analyticity Properties
		6-3-1 Landau Equations
		6-3-2 Real Singularities
		6-3-3 Real Singularities Of Simple Diagrams
		6-3-4 Physical-region Singularities. Cutkosky Rules
	Notes
Chapter Seven Radiative Corrections
	7-1 One-Loop Renormalization
		7-1-1 Vacuum Polarization
		7-1-2 Electron Propagator
		7-1-3 Vertex Function
		7-1-4 Summary
	7-2 Radiative Corrections To The Interaction With An External Field
		7-2-1 Effective Interaction And Anomalous Magnetic Moment
		7-2-2 Radiative Corrections To Coulomb Scattering
		7-2-3 Soft Bremsstrahlung
		7-2-4 Finite Inclusive Cross Section
	7-3 New Effects
		7-3-1 Photon-Photon Scattering
		7-3-2 Lamb Shift
		7-3-3 Van der Waals Forces At Large Distances
	Notes
Chapter Eight Renormalization
	8-1 Regularization And Power Counting
		8-1-1 Introduction
		8-1-2 Regularization
		8-1-3 Power Counting
		8-1-4 Convergence Theorem
	8-2 Renormalization
		8-2-1 Normalization Conditions And Structure Of The Counterterms
		8-2-2 Bogoliubov\'s Recursion Formula
		8-2-3 Zimmermann\'s Explicit Solution
		8-2-4 Renormalization In Parametric Space
		8-2-5 Finite Renormalizations
		8-2-6 Composite Operators
	8-3 Zero-Mass Limit, Asymptotic Behavior, And Weinberg\'s Theorem
		8-3-1 Massless Theories
		8-3-2 Ultraviolet Behavior And Weinberg\'s Theorem
	8-4 The Case Of Quantum Electrodynamics
		8-4-1 Formal Derivation Of The Ward-Takahashi Identities
		8-4-2 Pauli-Villars Regularization To All Orders
		8-4-3 Renormalization
		8-4-4 Two-Loop Vacuum Polarization
	Notes
Chapter Nine Functional Methods
	9-1 Path Integrals
		9-1-1 The Role Of The Classical Action In Quantum Mechanics
		9-1-2 Trajectories In The Bargmann-Fock Space
		9-1-3 Fermion Systems
	9-2 Relativistic Formulation
		9-2-1 S-Matrix And Green\'s Functions In Terms Of Path Integrals
		9-2-2 Effective Action And Steepest-Descent method
	9-3 Constrained Systems
		9-3-1 General Discussion
		9-3-2 The Electromagnetic Field As An Example
	9-4 Large Orders In Perturbation Theory
		9-4-1 Introduction
		9-4-2 Anharmonic Oscillator
	Notes
Chapter Ten Integral Equations And Bound-State Problems
	10-1 The Dyson-Schwinger Equations
		10-1-1 Field Equations
		10-1-2 Renormalization
	10-2 Relativistic Bound States
		10-2-1 Homogeneous Bethe-Salpeter Equations
		10-2-2 The Wick Rotation
		10-2-3 Scalar Massless Exchange In The Ladder Approximation
	10-3 Hyperfine Splitting In Positronium
		10-3-1 General Setting
		10-3-2 Calculation To Order Alpha(5)
	Notes
Chapter Eleven Symmetries
	11-1 Quantum Implimentation Of Symmetries
		11-1-1 Statement Of The Problem
		11-1-2 Behavior Of The Ground State
	11-2 Mass Spectrum, Multiplets, And Goldstone Bosons
		11-2-1 The Octet Model Of Gell-Mann And Ne\'eman
		11-2-2 Spontaneous Symmetry Breaking
	11-3 Current Algebra
		11-3-1 Current Commutators
		11-3-2 Approximate Conservation Of The Axial Current And Chiral Symmetry
		11-3-3 Low-Energy Theorems And Sum Rules
	11-4 The Sigma Model
		11-4-1 DescriptionOf The Model
		11-4-2 Renormalization
	11-5 Anomalies
		11-5-1 The Neutral Pion-Two-Photon Decay And Current Algebra
		11-5-2 The Axial Anomaly In The Sigma Model
		11-5-3 General Properties
	Notes
Chapter Twelve Nonabelian Gauge Fields
	12-1 Classical Theory
		12-1-1 The Gauge Field A-mu And The Tensor F-mu-nu
		12-1-2 Classical Dynamics
		12-1-3 Euclidean Solutions To The Classical Equations Of Motion
		12-1-4 Gauge Invariance And Constraints
	12-2 Quantization Of Gauge Fields
		12-2-1 Constrained Quantization
		12-2-2 Intergration Over The Gauge Group
		12-2-3 Feynman Rules
	12-3 The Effective Action At The One Loop Order
		12-3-1 Genral Form
		12-3-2 The Two-Point Function
		12-3-3 Other Functions
		12-3-4 One-Loop Renormalization
	12-4 Renormalization
		12-4-1 Slavnov-Taylor Identities
		12-4-2 Identities For Proper Functions
		12-4-3 Recursive Construction Of The Counterterms
		12-4-4  Gauge Dependence Of Green Functions
		12-4-5 Anomalies
	12-5 Massive Gauge Fields
		12-5-1 Historical Background
		12-5-2 Massive Gauge Theory
		12-5-3 Spontaneous Symmetry Breaking
		12-5-4 Renormalization Of Spontaneously Broken Gauge Theories
		12-5-5 Gauge Independence And Unitarity Of The S-Matrix
	12-6 The Weinberg-Salam Model
		12-6-1 The Model For Leptons
		12-6-2 Electron-Neutrino Cross Sections
		12-6-3 Higher-Order Corrections
		12-6-4 Incorporation Of Hadrons
	Notes
Chapter Thirteen Asymptotic Behavior
	13-1 Effective Charge In Electrodynamics
		13-1-1 The Gell-Mann And Low Function
		13-1-2 The Callan-Symanzik Equation
	13-2 Broken Scale Invariance
		13-2-1 Scale And Conformal Invariance
		13-2-2 Modified Ward Identities
		13-2-3 Callan-Symanzik CoefficientsTo Lowest Orders
	13-3 Scale Invariance Recovered
		13-3-1 Coupling Constant Flow
		13-3-2 Asymptotic Freedom
		13-3-3 Mass Corrections
	13-4 Deep Inelastic Lepton-Hadron Scattering And Electron-Positron Annihilation Into Hadrons
		13-4-1 Electroproduction
		13-4-2 Light-Cone Dynamics
		13-4-3 Electron-Positron Annihilation
	13-5 Operator Product Expansions
		13-5-1 Short-Distance Expansion
		13-5-2 Dominant And Subdominant Operators, Operator Mixing, And Conservation Laws
		13-5-3 Light-Cone Expansion
	Notes
Appendix
	A-1 Metric
	A-2 Dirac Matricies And Spinors
	A-3 Normalization Of States, S-Matrix, Unitarity, And Cross Sections
	A-4 Feynman Rules
Index
Errata
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