Quantum Field Theory

Häftad, Engelska, 2006

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This text offers a balanced treatment of quantum field theory, providing both formal presentation and numerous examples. It begins with the standard quantization of electrodynamics, culminating in the perturbative renormalization, and proceeds to functional methods, relativistic bound states, broken symmetries, nonabelian gauge fields, and asymptotic behavior. 157 figures. 1980 edition.

Produktinformation

Utgivningsdatum2006-03-31
Mått164 x 234 x 36 mm
Vikt1 000 g
FormatHäftad
SpråkEngelska
SerieDover Books on Physics
Antal sidor752
FörlagDover Publications Inc.
ISBN9780486445687

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PrefaceGeneral References1. Classical Theory1.1 Principle of Least Action1.1.1 Classical Motion1.1.2 Electromagnetic Field as an Infinite Dynamical System1.1.3 Electromagnetic Interaction of a Point Particle1.2 Symmetries and Conservation Laws1.2.1 Fundamental Invariants1.2.2 Energy Momentum Tensor1.2.3 Internal Symmetries1.3 Propagation and Radiation1.3.1 Green Functions1.3.2 Radiation2. The Dirac Equation2.1 Toward a Relativistic Wave Equation2.1.1 Quantum Mechanics and Relativity2.1.2 The Dirac Equation2.1.3 Relativistic Covariance2.2 Physical Content2.2.1 Plane Wave Solutions and Projectors2.2.2 Wave Packets2.2.3 Electromagnetic Coupling2.2.4 Foldy-Wouthuysen Transformation2.3 Hydrogen-like Atoms2.3.1 Nonrelativistic versus Relativistic Spectrum2.3.2 Dirac Theory2.4 Hole Theory and Charge Conjugation2.4.1 Reinterpretation of Negative Energy Solutions2.4.2 Charge Conjugation2.4.3 Zero-Mass Particles2.5 Dirac Propagator2.5.1 Free Propagator2.5.2 Propagation in an Arbitrary External Electromagnetic Field2.5.3 Application to the Coulomb Scattering2.5.4 Fock-Schwinger Proper Time Method3. Quantization--Free Fields3.1 Canonical Quantization3.1.1 General Formulation3.1.2 Scalar Field3.1.3 Charged Scalar Field3.1.4 Time-Ordered Product3.1.5 Thermodynamic Equilibrium3.2 Quantized Radiation Field3.2.1 Indefinite Metric3.2.2 Propagator3.2.3 Massive Vector Field3.2.4 Vacuum Fluctuations3.3 Dirac Field and Exclusion Principle3.3.1 Anticommutators3.3.2 Fock Space for Fermions3.3.3 Relation between Spin and Statistics--Propagator3.4 Discrete Symmetries3.4.1 Parity3.4.2 Charge Conjugation3.4.3 Time Reversal3.4.4 Summary4. Interaction with an External Field4.1 Quantized Electromagnetic Field Interacting with a Classical Source4.1.1 Emission Probabilities4.1.2 Emitted Energy and the Infrared Catastrophe4.1.3 Induced Absorption and Emission4.1.4 S Matrix and Evolution Operator4.2 Wick's Theorem4.2.1 Bose Fields4.2.2 Fermi Fields4.2.3 General Case4.3 Quantized Dirac Field Interacting with a Classical Potential4.3.1 General Formalism4.3.2 Emission Rate to Lowest Order4.3.3 Pair Creation in a Constant Uniform Electric Field4.3.4 The Euler-Heisenberg Effective Lagrangian5. Elementary Processes5.1 S Matrix and Asymptotic Theory5.1.1 Cross Sections5.1.2 Asymptotic Theory5.1.3 Reduction Formulas5.1.4 Generating Functional5.1.5 Connected Parts5.1.6 Fermions5.1.7 Photons5.2 Applications5.2.1 Compton Effect5.2.2 Pair Annihilation5.2.3 Positronium Lifetime5.2.4 Bremsstrahlung5.3 Unitarity and Causality5.3.1 Unitarity and Partial Wave Decomposition5.3.2 Causality and Analyticity5.3.3 The Jost-Lehmann-Dyson Representation5.3.4 Forward Dispersion Relations5.3.5 Momentum Transfer Analyticity6. Perturbation Theory6.1 Interaction Representation and Feynman Rules6.1.1 Self-Interacting Scalar Field6.1.2 Feynman Rules for Spinor Electrodynamics6.1.3 Electron-Electron and Electron-Positron Scattering6.1.4 Scalar Electrodynamics6.2 Diagrammatics6.2.1 Loopwise Expansion6.2.2 Truncated and Proper Diagrams6.2.3 Parametric Representation6.2.4 Euclidean Green Functions6.3 Analyticity Properties6.3.1 Landau Equations6.3.2 Real Singularities6.3.3 Real Singularities of Simple Diagrams6.3.4 Physical-Region Singularities. Cutkosky Rules7. Radiative Corrections7.1 One-Loop Renormalization7.1.1 Vacuum Polarization7.1.2 Electron Propagator7.1.3 Vertex Function7.1.4 Summary7.2 Radiative Corrections to the Interaction with an External Field7.2.1 Effective Interaction and Anomalous Magnetic Moment7.2.2 Radiative Corrections to Coulomb Scattering7.2.3 Soft Bremsstrahlung7.2.4 Finite Inclusive Cross Section7.3 New Effects7.3.1 Photon-Photon Scattering7.3.2 Lamb Shift7.3.3 Van der Waals Forces at Large Distances8. Renormalization8.1 Regularization and Power Counting8.1.1 Introduction8.1.2 Regularization8.1.3 Power Counting8.1.4 Convergence Theorem8.2 Renormalization8.2.1 Normalization Conditions and Structure of the Counterterms8.2.2 Bogoliubov's Recursion Formula8.2.3 Zimmermann's Explicit Solution8.2.4 Renormalization in Parametric Space8.2.5 Finite Renormalizations8.2.6 Composite Operators8.3 Zero-Mass Limit, Asymptotic Behavior, and Weinberg's Theorem8.3.1 Massless Theories8.3.2 Ultraviolet Behavior and Weinberg's Theorem8.4 The Case of Quantum Electrodynamics8.4.1 Formal Derivation of the Ward-Takahashi Identities8.4.2 Pauli-Villars Regularization to All Orders8.4.3 Renormalization8.4.4 Two-Loop Vacuum Polarization9. Functional Methods9.1 Path Integrals9.1.1 The Role of the Classical Action in Quantum Mechanics9.1.2 Trajectories in the Bargmann-Fock Space9.1.3 Fermion Systems9.2 Relativistic Formulation9.2.1 S Matrix and Green Functions in Terms of Path Integrals9.2.2 Effective Action and Steepest-Descent Method9.3 Constrained Systems9.3.1 General Discussion9.3.2 The Electromagnetic Field as an Example9.4 Large Orders in Perturbation Theory9.4.1 Introduction9.4.2 Anharmonic Oscillator10. Integral Equations and Bound-State Problems10.1 The Dyson-Schwinger Equations10.1.1 Field Equations10.1.2 Renormalization10.2 Relativistic Bound States10.2.1 Homogeneous Bethe-Salpeter Equation10.2.2 The Wick Rotation10.2.3 Scalar Massless Exchange in the Ladder Approximation&n12.3 The Effective Action at the One-Loop Order12.3.1 General Form12.3.2 Two-Point Function12.3.3 Other Functions12.3.4 One-Loop Renormalization12.4 Renormalization12.4.1 Slavnov-Taylor Identities12.4.2 Identities for Proper Functions12.4.3 Recursive Construction of the Counterterms12.4.4 Gauge Dependence of Green Functions12.4.5 Anomalies12.5 Massive Gauge Fields12.5.1 Historical Background12.5.2 Massive Gauge Theory12.5.3 Spontaneous Symmetry Breaking12.5.4 Renormalization of Spontaneously Broken Gauge12.5.5 Gauge Independence and Unitarity of the S Matrix12.6 The Weinberg-Salam Model12.6.1 The Model for Leptons12.6.2 Electron-Neutrino Cross Sections12.6.3 Higher-Order Corrections12.6.4 Incorporation of Hadrons13. Asymptotic Behavior13.1 Effective Charge in Electrodynamics13.1.1 The Gell-Mann and Low Function13.1.2 The Callan-Symanzik Equation13.2 Broken Scale Invariance13.2.1 Scale and Conformal Invariance13.2.2 Modified Ward Identities13.2.3 Callan-Symanzik Coefficients to Lowest Order13.3 Scale Invariance Recovered13.3.1 Coupling Constant Flow13.3.2 Asymptotic Freedom13.3.3 Mass Corrections13.4 Deep Inelastic Lepton-Hadron Scattering and Electron-Positron Annihilation into Hadrons13.4.1 Electroproduction13.4.2 Light-Cone Dynamics13.4.3 Electron-Positron Annihilation13.5 Operator Product Expansions13.5.1 Short-Distance Expansion13.5.2 Dominant and Subdominant Operators, Operator Mixing, and Conservation Laws13.5.3 Light-Cone ExpansionAppendixA-1 MetricA-2 Dirac Matrices and SpinorsA-3 Normalization of States, S Matrix, Unitarity, and Cross SectionsA-4 Feynman RulesIndex