Preface |
Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics / I: |
The Particles and Forces of the Standard Model / 1: |
Introduction: the Standard Model / 1.1: |
The fermions of the Standard Model / 1.2: |
Leptons / 1.2.1: |
Quarks / 1.2.2: |
Particle interactions in the Standard Model / 1.3: |
Classical and quantum fields / 1.3.1: |
The Yukawa theory of force as virtual quantum exchange / 1.3.2: |
The one-quantum exchange amplitude / 1.3.3: |
Electromagnetic interactions / 1.3.4: |
Weak interactions / 1.3.5: |
Strong interactions / 1.3.6: |
The gauge bosons of the Standard Model / 1.3.7: |
Renormalization and the Higgs sector of the Standard Model / 1.4: |
Renormalization / 1.4.1: |
The Higgs boson of the Standard Model / 1.4.2: |
Summary / 1.5: |
Problems |
Electromagnetism as a Gauge Theory / 2: |
Introduction / 2.1: |
The Maxwell equations: current conservation / 2.2: |
The Maxwell equations: Lorentz covariance and gauge invariance / 2.3: |
Gauge invariance (and covariance) in quantum, mechanics / 2.4: |
The argument reversed: the gauge principle / 2.5: |
Comments on the gauge principle in electromagnetism / 2.6: |
Relativistic Quantum Mechanics / 3: |
The Klein-Gordon equation / 3.1: |
Solutions in coordinate space / 3.1.1: |
Probability current for the KG equation / 3.1.2: |
The Dirac equation / 3.2: |
Free-particle solutions / 3.2.1: |
Probability current for the Dirac equation / 3.2.2: |
Spin / 3.3: |
The negative-energy solutions / 3.4: |
Positive-energy spinors / 3.4.1: |
Negative-energy spinors / 3.4.2: |
Dirac's interpretation of the negative-energy solutions of the Dirac equation / 3.4.3: |
Feynman's interpretation of the negative-energy solutions of the KG and Dirac equations / 3.4.4: |
Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron / 3.5: |
Lorentz Transformations and Discrete Symmetries / 4: |
Lorentz transformations / 4.1: |
The KG equation / 4.1.1: |
Discrete transformations: P, C and T / 4.1.2: |
Parity / 4.2.1: |
Charge conjugation / 4.2.2: |
CP / 4.2.3: |
Time reversal / 4.2.4: |
CPT / 4.2.5: |
Introduction to Quantum Field Theory / II: |
Quantum Field Theory I: The Free Scalar Field / 5: |
The quantum field: (i) descriptive / 5.1: |
The quantum field: (ii) Lagrange-Hamilton formulation / 5.2: |
The action principle: Lagrangian particle mechanics / 5.2.1: |
Quantum particle mechanics a la Heisenberg-Lagrange-Hamilton / 5.2.2: |
Interlude: the quantum oscillator / 5.2.3: |
Lagrange-Hamilton classical field mechanics / 5.2.4: |
Heisenberg-Lagrange-Hamilton quantum field mechanics / 5.2.5: |
Generalizations: four dimensions, relativity and mass / 5.3: |
Quantum Field Theory II: Interacting Scalar Fields / 6: |
Interactions in quantum field theory: qualitative introduction / 6.1: |
Perturbation theory for interacting fields: the Dyson expansion of the S-matrix / 6.2: |
The interaction picture / 6.2.1: |
The 5-matrix and the Dyson expansion / 6.2.2: |
Applications to the 'ABC theory / 6.3: |
The decay C → A + B / 6.3.1: |
A + B → A + B scattering: the amplitudes / 6.3.2: |
A + B → A + B scattering: the Yukawa exchange mechanism, s and u channel processes / 6.3.3: |
A + B → A + B scattering: the differential cross section / 6.3.4: |
A + B → A +'B scattering: loose ends / 6.3.5: |
Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields; Introduction of Electromagnetic Interactions / 7: |
The complex scalar field: global U(1) phase invariance, particles and antiparticles / 7.1: |
The Dirac field and the spin-statistics connection / 7.2: |
The Maxwell field Aμ (x) / 7.3: |
The classical field case / 7.3.1: |
Quantizing Aμ(x) / 7.3.2: |
Introduction of electromagnetic interactions / 7.4: |
P, C and T in quantum field theory / 7.5: |
Tree-Level Applications in QED / 7.5.1: |
Elementary Processes in Scalar and Spinor Electrodynamics / 8: |
Coulomb scattering of charged spin-0 particles / 8.1: |
Coulomb scattering of s+ (wavefunction approach) / 8.1.1: |
Coulomb scattering of s+ (field-theoretic approach) / 8.1.2: |
Coulomb scattering of s- / 8.1.3: |
Coulomb scattering of charged spin-1/2 particles / 8.2: |
Coulomb scattering of e- (wavefunction approach) / 8.2.1: |
Coulomb scattering of e- (field-theoretic approach) / 8.2.2: |
Trace techniques for spin summations / 8.2.3: |
Coulomb scattering of e+ / 8.2.4: |
e-s+ scattering / 8.3: |
The amplitude for e-s+ → e-s+ / 8.3.1: |
The cross section for e-s+ → e-s+ / 8.3.2: |
Scattering from a non-point-like object: the pion form factor in e-π+ → e-π+ / 8.4: |
e- scattering from a charge distribution / 8.4.1: |
Lorentz invariance / 8.4.2: |
Current conservation / 8.4.3: |
The form factor in the time-like region: e+e- → π+π- and crossing symmetry / 8.5: |
Electron Compton scattering / 8.6: |
The lowest-order amplitudes / 8.6.1: |
Gauge invariance / 8.6.2: |
The Compton cross section / 8.6.3: |
Electron muon elastic scattering / 8.7: |
Electron-proton elastic scattering and nucleon form factors / 8.8: |
Deep Inelastic Electron-Nucleon Scattering and the Parton Model / 8.8.1: |
Inelastic electron-proton scattering: kinematics and structure functions / 9.1: |
Bjorken scaling and the parton model / 9.2: |
Partons as quarks and gluons / 9.3: |
The Drell-Yan process / 9.4: |
e+e- annihilation into hadrons / 9.5: |
Loops and Renormalization / IV: |
Loops and Renormalization I: The ABC Theory / 10: |
The propagator correction in ABC theory / 10.1: |
The Ο(g2) self-energy ΠC[2] (q2) / 10.1.1: |
Mass shift / 10.1.2: |
Field strength renormalization / 10.1.3: |
The vertex correction / 10.2: |
Dealing with the bad news: a simple example / 10.3: |
Evaluating ΠC[2] (q2) / 10.3.1: |
Regularization and renormalization / 10.3.2: |
Bare and renormalized perturbation theory / 10.4: |
Reorganizing perturbation theory / 10.4.1: |
The Ο(gph2) renormalized self-energy revisited: how counter terms are determined by renormalization conditions / 10.4.2: |
Renormalizability / 10.5: |
Loops and Renormalization II: QED / 11: |
Counter terms / 11.1: |
The Ο(e2) fermion self-energy / 11.2: |
The Ο (e2) photon self-energy / 11.3: |
The Ο (e2) renormalized photon self-energy / 11.4: |
The physics of Πγ[2] (q2) / 11.5: |
Modified Coulomb's law / 11.5.1: |
Radiatively induced charge form factor / 11.5.2: |
The running coupling constant / 11.5.3: |
ΠC[2] in the s-channel / 11.5.4: |
The Ο(e2) vertex correction, and Z1 = Z2 / 11.6: |
The anomalous magnetic moment and tests of QED / 11.7: |
Which theories are renormalizable - and does it matter? / 11.8: |
Non-relativistic Quantum Mechanics / A: |
Natural Units / B: |
Maxwell's Equations: Choice of Units / C: |
Special Relativity: Invariance and Covariance / D: |
Dirac 5-Function / E: |
Contour Integration / F: |
Green Functions / G: |
Elements of Non-relativistic Scattering Theory / H: |
Time-independent formulation and differential cross section / H.1: |
Expression for the scattering amplitude: Born approximation / H.2: |
Time-dependent approach / H.3: |
The Schrodinger and Heisenberg Pictures |
Dirac Algebra and Trace Identities / J: |
Dirac algebra / J.1: |
γ matrices / J.1.1: |
γ5 identities / J.1.2: |
Hermitian conjugate of spinor matrix elements / J.1.3: |
Spin sums and projection operators / J.1.4: |
Trace theorems / J.2: |
Example of a Cross Section Calculation / K: |
The spin-averaged squared matrix element / K.1: |
Evaluation of two-body Lorentz-invariant phase space in 'laboratory' variables / K.2: |
Feynman Rules for Tree Graphs in QED / L: |
External particles / L.1: |
Propagators / L.2: |
Vertices / L.3: |
References |
Index |
Preface |
Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics / I: |
The Particles and Forces of the Standard Model / 1: |