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Week I
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January 14–18
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An introduction to the particles and forces of nature (gravity, electromagnetism, the weak force, the strong force); Yukawa’s force; matter (leptons and quarks)
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Week II
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January 21–25
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Symmetries; the Lorentz group; boosts; the Minkowski metric; Poincaré transformations; particle kinematics; properties of Lorentz transformations: lack of simultaneity, Lorentz contractions, time dilations, velocity addition
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Week III
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Jan 28–Feb 1
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Energy and momentum; massless particles; colliding particles; symmetries, invariant tensors; rotations; parity; the orthogonal group; the definition of a group; representations of the Lorentz group: scalars, vectors, tensors
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Week IV
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February 4–8
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The action and Lagrangian; how to build a particle action; angular momentum; angular momentum eigenstates; raising and lowering operators; spin; SU(2)
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Week V
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February 11–15
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Nonrelativistic fermions; representations of SU(2); products of representations; the Clebsch-Gordan decomposition; tensor representations; isospin SU(2)
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Week VI
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February 18–22
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Discrete symmetries; parity; quantum numbers; parity violation; Wu’s experiment; charge conjugation; G-parity; CP-violation; the Fitch-Cronin experiment; time-reversal
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Week VII
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Feb 25–March 1
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Fermions; generators of the Lorentz group; (s+,s–) representations, how to build a relativistic action for fermions; Weyl equation; Weyl spinors
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Week VIII
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March 4–6
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Dirac spinors; γ-matrices [Midterm examination]
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Week IX
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March 18–22
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Fermion bilinears; Dirac’s equation and its solutions; electrons and positrons; Quantum Electrodynamics; Fμν; the vector field Aμ; the action for the photon; coupling light with matter; charge; gauge symmetries; gauge fixing; photon polarization; the completeness relation
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Week X
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March 25–29
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The Feynman rules; propagators and vertices; Møller scattering; perturbation theory; a list of scattering processes in QED; spin sums and spin averages; the fermion completeness relation; traces of γ-matrices
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Week XI
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April 1–5
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Scatterings and decays; decays (Γ); the cross-section (σ); the geometry of a scattering; the differential cross-section; inclusive and exclusive cross-sections; luminosity; Fermi’s Golden Rule (phase space); Γ for a decay into two particles
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Week XII
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April 8–12
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Scattering; two-body scattering; Quantum Chromodynamics; the electrodynamics of quarks at high energies (R); non-Abelian gauge theories; SU(2), SU(3)
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Week XIII
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April 15–17
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The gauge-invariant kinetic energy; the Feynman rules for QCD; pair annihilation (q-qbar to glue-glue)
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Week XIV
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April 22–26
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Tensor representations of SU(3); Young tableaux; Weak interactions; chiral fermions; several odd things about the weak interactions; SU(2)L; charged currents; electroweak mixing; the origin of mass; mixings amongst different generations
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Week XV
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April 29–May 3
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Mass eigenstates and gauge eigenstates; the origin of CP-violation in the standard model; spontaneous symmetry breaking; the Abelian Higgs model; the genuine SU(2) Higgs model
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