Format:
1 Online-Ressource (XXII, 842 Seiten)
ISBN:
9780429972102
Series Statement:
Frontiers in Physics
Content:
Cover -- Half Title -- Title -- Copyright -- Contents -- Preface -- Notations and Conventions -- Editor's Foreword -- Part I: Feynman Diagrams and Quantum Electrodynamics -- 1 Invitation: Pair Production in e + e - Annihilation -- 2 The Klein-Gordon Field -- 2.1 The Necessity of the Field Viewpoint -- 2.2 Elements of Classical Field Theory -- Lagrangian Field Theory -- Hamiltonian Field Theory -- Noether's Theorem -- 2.3 The Klein-Gordon Field as Harmonic Oscillators -- 2.4 The Klein-Gordon Field in Space-Time -- Causality -- The Klein-Gordon Propagator -- Particle Creation by a Classical Source -- Problems -- 3 The Dirac Field -- 3.1 Lorentz Invariance in Wave Equations -- 3.2 The Dirac Equation -- Weyl Spinors -- 3.3 Free-Particle Solutions of the Dirac Equation -- Spin Sums -- 3.4 Dirac Matrices and Dirac Field Bilinears -- 3.5 Quantization of the Dirac Field -- Spin and Statistics -- The Dirac Propagator -- 3.6 Discrete Symmetries of the Dirac Theory -- Parity -- Time Reversal -- Charge Conjugation -- Problems -- 4 Interacting Fields and Feynman Diagrams -- 4.1 Perturbation Theory-Philosophy and Examples -- 4.2 Perturbation Expansion of Correlation Functions -- 4.3 Wick's Theorem -- 4.4 Feynman Diagrams -- 4.5 Cross Sections and the S-Matrix -- 4.6 Computing S-Matrix Elements from Feynman Diagrams -- 4.7 Feynman Rules for Fermions -- Yukawa Theory -- 4.8 Feynman Rules for Quantum Electrodynamics -- The Coulomb Potential -- Problems -- 5 Elementary Processes of Quantum Electrodynamics -- 5.1 e + e - → μ + μ - : Introduction -- Trace Technology -- Unpolarized Cross Section -- e+ e- → Hadrons -- 5.2 e+ e- → μ + μ - : Helicity Structure -- 5.3 e+ e- → μ + μ - : Nonrelativistic Limit -- Bound States -- Vector Meson Production and Decay -- 5.4 Crossing Symmetry -- Electron-Muon Scattering -- Mandelstam Variables -- 5.5 Compton Scattering
Content:
Photon Polarization Sums -- The Klein-Nishina Formula -- High-Energy Behavior -- Pair Annihilation into Photons -- Problems -- 6 Radiative Corrections: Introduction -- 6.1 Soft Bremsstrahlung -- Classical Computation -- Quantum Computation -- 6.2 The Electron Vertex Function: Formal Structure -- 6.3 The Electron Vertex Function: Evaluation -- Feynman Parameters -- Precision Tests of QED -- 6.4 The Electron Vertex Function: Infrared Divergence -- 6.5 Summation and Interpretation of Infrared Divergences -- Problems -- 7 Radiative Corrections: Some Formal Developments -- 7.1 Field-Strength Renormalization -- The Electron Self-Energy -- 7.2 The LSZ Reduction Formula -- 7.3 The Optical Theorem -- The Optical Theorem for Feynman Diagrams -- Unstable Particles -- 7.4 The Ward-Takahashi Identity -- 7.5 Renormalization of the Electric Charge -- Dimensional Regularization -- Problems -- Final Project: Radiation of Gluon Jets -- Part II: Renormalization -- 8 Invitation: Ultraviolet Cutoffs and Critical Fluctuations -- 9 Functional Methods -- 9.1 Path Integrals in Quantum Mechanics -- 9.2 Functional Quantization of Scalar Fields -- Correlation Functions -- Feynman Rules -- Functional Derivatives and the Generating Functional -- 9.3 Quantum Field Theory and Statistical Mechanics -- 9.4 Quantization of the Electromagnetic Field -- 9.5 Functional Quantization of Spinor Fields -- Anticommuting Numbers -- The Dirac Propagator -- Generating Functional for the Dirac Field -- QED -- Functional Determinants -- 9.6 Symmetries in the Functional Formalism -- Equations of Motion -- Conservation Laws -- The Ward-Takahashi Identity -- Problems -- 10 Systematics of Renormalization -- 10.1 Counting of Ultraviolet Divergences -- 10.2 Renormalized Perturbation Theory -- One-Loop Structure of ϕ4 Theory -- 10.3 Renormalization of Quantum Electrodynamics -- One-Loop Structure of QED
Content:
10.4 Renormalization Beyond the Leading Order -- 10.5 A Two-Loop Example -- Problems -- 11 Renormalization and Symmetry -- 11.1 Spontaneous Symmetry Breaking -- The Linear Sigma Model -- Goldstone's Theorem -- 11.2 Renormalization and Symmetry: An Explicit Example -- 11.3 The Effective Action -- 11.4 Computation of the Effective Action -- The Effective Action in the Linear Sigma Model -- 11.5 The Effective Action as a Generating Functional -- 11.6 Renormalization and Symmetry: General Analysis -- Goldstone's Theorem Revisited -- Problems -- 12 The Renormalization Group -- 12.1 Wilson's Approach to Renormalization Theory -- 12.2 The Callan-Symanzik Equation -- Renormalization Conditions -- The Callan-Symanzik Equation -- Computation of β and γ -- The Meaning of β and γ -- 12.3 Evolution of Coupling Constants -- Solution of the Callan-Symanzik Equation -- An Application to QED -- Alternatives for the Running of Coupling Constants -- 12.4 Renormalization of Local Operators -- 12.5 Evolution of Mass Parameters -- Critical Exponents: A First Look -- Problems -- 13 Critical Exponents and Scalar Field Theory -- 13.1 Theory of Critical Exponents -- Exponents of the Spin Correlation Function -- Exponents of Thermodynamic Functions -- Values of the Critical Exponents -- 13.2 Critical Behavior in Four Dimensions -- 13.3 The Nonlinear Sigma Model -- Problems -- Final Project: The Coleman-Weinberg Potential -- Part III: Non-Abelian Gauge Theories -- 14 Invitation: The Parton Model of Hadron Structure -- 15 Non-Abelian Gauge Invariance -- 15.1 The Geometry of Gauge Invariance -- 15.2 The Yang-Mills Lagrangian -- 15.3 The Gauge-Invariant Wilson Loop -- 15.4 Basic Facts About Lie Algebras -- Classification of Lie Algebras -- Representations -- The Casimir Operator -- Problems -- 16 Quantization of Non-Abelian Gauge Theories
Additional Edition:
Erscheint auch als Druck-Ausgabe, Paperback Peskin, Michael E An introduction to quantum field theory Boulder : Chapman and Hall/CRC,c2018 ISBN 978-0-201-50397-5
Additional Edition:
ISBN 0-201-50397-2
Language:
English
Subjects:
Physics
Keywords:
Quantenfeldtheorie
Author information:
Schroeder, Daniel V. 1962-
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