| Date |
Tuesday |
Thursday |
| Aug. 29, 31 |
1,2; 1.1,2
a bit of history, concept of quantum
field and vacuum, harmonic oscillator, Lagrangian
formulation of small amplitude string motion |
1,2; 1.1,2,4,5
quantum scalar field |
| Sept. 5, 7 |
1.6,7,8; vacuum energy, Fock space; review of special relativity (notes) |
more
relativity |
| Sept. 12, 14 |
1.10,11
Heisenberg picture, causality |
2.1,2.2 Feynman
propagator, interacting vacuum, Kallen-Lehmann
representation |
| Sept. 19, 21 |
6, 2.3,4
S-matrix,
asymptotic states, LSZ reduction formula |
7, 2.5
interaction picture |
| Sept. 26, 28 |
7,
2.5-10 Wick's theorem,
diagrammatic expansion, Feynman
rules |
2.9,10
1PI diagrams, dressed
propagator, Feynman rules for S-matrix |
| Oct. 3, 5 |
5, 7, 2.11 tree-level 2-2 scattering in theory, Mandelstam parameters, cross-sections | 5, 2.11
2-body phase space;
decay rates |
| Oct. 10, 12 |
8 spin-1 field with nonzero mass | 10 massless
spin-1 field, gauge invariance, gauge covariant
derivative |
| Oct. 17, 19 |
10, 11 spinors; Dirac equation, Weyl equation, Dirac matrices; SL(2,C) double cover of SO(3,1) | 10, 11 spinors; L & R
representations of the Lorentz group; Lorentz
invariance of the action; Majorana mass term |
| Oct. 24, 26 |
12 complex mass parameters, CP
violating phases in mass matrix, Euler-Lagrange
equations for complex field variables,
quantizing spinors, T-ordering fermions, Lorentz
invariance of Feynman propagator |
12 positive energy &
anticommutators, negative vacuum energy, phase
invariance & charge conservation,
anti-particles, gauge-covariant
derivative, gauge-invariant em action |
| Oct. 31, Nov. 2 |
13 Higgs mechanism; QED, Feyn. rules | 13 QED; cross section for
electron-positron scattering to hadrons;
asymptotic freedom |
| Nov. 7, 9 |
Compton
scattering |
radiative
corrections |
| Nov. 14, 16 |
Lamb shift |
|
| Nov. 21, 23 |
renormalized
charge in QED, momentum dependence of potential,
effective charge |
|
| Nov. 28, 30 |
continuation of last class, beta
function for QED, Landau pole |
non-Abelian gauge theory, beta
function for QCD, asymptotic freedom |
| Dec. 5, 7 |
coupling constant unification, renormalized perturbation theory | Classification of renormalizable theories, effective field theories, hierarchy problem |