| Date |
Notes |
| Wednesday 8/24 |
Introductions, course policies. Inspirational reading
(handout): F. Wilczek, "Quantum Field Theory",
Rev. Mod. Phys. 71, S85 (1999),
also available as hep-th/9803075.
|
| Friday 8/26 |
Review of Lagrangian and Hamiltonian formulation of particle dynamics.
Generalization to classical field theory. Derivation of the Euler-Lagrange equations.
Hamiltonian field theory.
|
| Monday 8/29 |
Example: Klein-Gordon action. Klein-Gordon equation. Hamiltonian description.
Begin derivation of Noether's theorem.
|
| Wednesday 8/31 |
Finish derivation of Noether's theorem.
|
| Friday 9/2 |
Symmetries and conservation laws. Translations, rotations,
internal U(1) symmetry.
|
| Monday 9/5 |
Labor Day - no class.
|
| Wednesday 9/7 |
Second quantization. Quantization conditions.
Review of QM of simple harmonic oscillator.
Ladder operators and their commutation relations.
|
| Friday 9/9 |
Consistency check of the quantization conditions.
Derivation of the Hamiltonian in terms of the ladder operators.
Eigenstates of the Hamiltonian and the momentum operator.
Particle interpretation.
|
| Monday 9/12 |
Statistics. Lorentz invariant measure. Comparison of conventions.
Heisenberg representation.
|
| Wednesday 9/14 |
Causality. Time ordered product. Feynman propagator.
|
| Friday 9/16 |
Derivation of the Feynman propagator for a scalar field.
|
| Monday 9/19 |
Lorentz invariance of the Lagrangian and the field equations
for the scalar and electromagnetic field. (Chapter 3.1).
Introduction to groups. Examples of finite (discrete) groups.
|
| Wednesday 9/21 |
Examples of continuous groups: O(2), SO(2), U(1), O(3) and SO(3).
The importance of generators.
|
| Friday 9/23 |
Algebra of the generators. The group SU(2).
Representation of spatial rotations in terms of SU(2).
The Lorentz group: generators of rotations and their algebra.
|
| Monday 9/26 |
The Lorentz group: generators of boosts and their algebra.
The SU(2)xSU(2) structure of the Lorentz group. Algebra of the A and B generators.
(1/2,0) and (0,1/2) Weyl spinors and their transformation properties.
Weyl equations.
|
| Wednesday 9/28 |
Helicity. Building Lorentz-invariant objects out of Weyl spinors.
Reality properties. Majorana spinors.
The Dirac Lagrangian and its symmetries (see Problem 3 from HW Set No. 5).
|
| Friday 9/30 |
Free-particle solutions of the Dirac equation.
(Chapter 3.3) Dirac spinors and the Klein-Gordon equation.
Plane-wave solutions. u and v spinors: general form.
|
| Monday 10/3 |
Normalization conditions for u and v spinors.
Spin sums (end of Section 3.3).
|
| Wednesday 10/5 |
Quantization of the Dirac field (Section 3.5).
|
| Friday 10/7 |
Homecoming - no class.
|
| Monday 10/10 |
The spin of a Dirac particle. Angular momentum from Noether's theorem.
Angular momentum operator and its eigenvalues.
|
| Wednesday 10/12 |
Interaction Lagrangians. Requirements. Dimensional analysis.
Examples: phi-fourth, Yukawa, QED. Gauge invariance. Covariant derivatives.
|
| Friday 10/14 |
Section 4.2: Perturbation expansion of correlation functions:
Free scalar field in the Schrodinger and Heisenberg picture, interacting scalar field.
Time evolution operator U(t,t0). The differential equation for U and its solution.
Time-ordering and exponentiating the solution. Eq. (4.31).
|
| Monday 10/17 |
Section 4.3: Wick's theorem. Normal ordering versus time ordering.
Contractions. Simple Feynman diagrams. Feynman diagrams (section 4.4).
2-point correlation function including interactions. Combinatorics of
the first-order term. Symmetry factors.
|
| Wednesday 10/19 |
Feynman rules for phi-fourth theory. Example of a third-order term.
Feynman rules in momentum space. Connected versus disconnected diagrams.
Examples of factorizing the vacuum bubbles: a 2-point function,
a 4-point function. Feynman rules in momentum space:
momentum conservation at each vertex, factors at external points.
|
| Friday 10/21 |
Cross-sections (section 4.5). Definitions. S-matrix. T-matrix.
The general formula for 2 to N scattering. Decay rates. 2-body phase space.
Formula for 2 to 2 scattering in the CM frame.
Simplified version for the case of equal masses.
|
| Monday 10/24 |
Calculation of T-matrix elements in terms of Feynman diagrams.
Examples of disconnected diagrams. Amputated diagrams.
Contractions with external states.
Example: the first order term in the 2 to 2 amplitude in phi-fourth theory.
2 to 2 cross-section in phi-fourth theory.
An improved version of the Feynman rules for phi-fourth theory.
|
| Wednesday 10/26 |
Feynman rules. Propagators for spin 0, 1/2, 1 and 2 particles.
|
-
| Friday 10/28 |
Vertices. External fermions. External photons. Minus sign rules for fermions.
Elementary processes of QED. Begin calculation of the matrix element
squared for electron-positron annihilation into muon pairs.
|
| Monday 10/31 |
Finish the calculation of the cross-section for e+ e- into mu+ mu-.
Spin sums and averaging. Trace technology of gamma matrices.
The differential cross-section in terms of the scattering angle.
|
| Wednesday 11/2 |
Mandelstam variables. Crossing symmetry. Electron-muon scattering.
|
| Friday 11/4 |
Compton scattering. Spin sums for photons. Organising the calculation.
Evaluation of traces.
|
| Monday 11/7 |
Finish the calculation of Compton scattering.
|
| Wednesday 11/9 |
Crossing symmetry: e+ e- annihilation into photons.
High energy limit.
|
| Friday 11/11 |
Field trip:
SESAPS meeting and
UF-FSU particle physics workshop.
|
| Monday 11/14 |
Discussion of singularities in the s,t and u channels.
Monte Carlo integration methods and their application in particle physics.
|
| Wednesday 11/16 |
Introduction to CompHEP. CompHEP tutorial.
|
| Friday 11/18 |
Types of radiative corrections. Ultraviolet and infrared divergences.
Quantum computation of soft bremsstrahlung.
|
| Monday 11/21 |
Section 6.2: The electron vertex function: formal structure.
Consequences from Lorentz and gauge invariance. Form factors.
Electric charge and magnetic moment of the electron.
|
| Wednesday 11/23 |
PYTHIA tutorial.
|
| Friday 11/25 |
Thanksgiving holiday - no class.
|
| Monday 11/28 |
Section 6.3: The electron vertex function: evaluation. Feynman parameters.
Manipulation of the denominator.
|
| Wednesday 11/30 |
Evaluation of loop integrals. Teaching evaluations.
|
| Friday 12/2 |
Pauli-Villars regularization. Finish the calculation of the electron vertex function.
|
| Monday 12/5 |
Section 6.4 The electron vertex function: IR cancellation.
|
| Wednesday 12/7 |
Last lecture: distribute
final exam.
Overview of past homework problems.
|