Tutorials

Tutorial #1   []	Handout   Solutions
Notation, Lorentz invariance, Index gymnastics, Dirac delta function.
Tutorial #2   []	Handout   Notes   Solutions
Natural Units and Dimensional Analysis. SR recap II. Ladder operators and Heisenberg algebra.
Tutorial #3   []	Handout   Fields overview   Solutions
Fourier Transform. The Lagrangian of the real scalar (KGF) field.
Tutorial #4   []	Notes
Group theory. Invariance in form and value. Rotations in Euclidean 3D space and the deffnition of a group. The Lorentz group. The unitary group. The generators of a group of differentiable transformations.
Tutorial #5   []	Handout   Part 1   Part 2
Part I. The quantization procedure. The inverse operator expansion. The evaluation of the commutator [a,a†]. The evaluation of the equal time commutator for the fields.
Tutorial #6   []	Handout   Solutions   Overview
Part II. The expansion of the Hamiltonian. An introduction to the infinite contributions to the energy and the normal ordering of operators. (Additional references: Casimir effect.) Symmetries and Conservation Laws. Noether’s theorem. (Additional references: Chapter 8 from Hagen Kleinert's Book on Particles and Quantum Fields)
Tutorial #7   []	Handout I & II   Solutions   Notes
The Dirac field, Part I. Gamma matrices (Dirac equation), Dirac algebra. Part II. Lorentz invariance of the Dirac equation. The Dirac equation for a free particle. Properties of the energy projection operator. Additional problems.
Tutorial #8   []	Solutions
Dirac field and gamma matrices (contd). Maxwell field, gauge fixing. Highlights from Problem Set 1.
Tutorial #9   []	Handout   Solutions
The Schrödinger, Heisenberg and Interaction Pictures. Perturbation Expansion of the S-Matrix. Wick’s Theorem. QED processes at 2nd order. (Additional references: The Schrodinger, Heisenberg and Interaction Pictures in QFT, Invariant commutation and propagation functions)
Tutorial #10   []	Solutions, Feynman diagrams
Problems 7.1, 7.3 and 7.5 (Mandl & Shaw), Feynman amplitudes for QED.
Tutorial #11   []	Handout   Solutions
Cross-sections. The relativistic definition of flux. The spin-sums lemma. The e-e+ production in electromagnetic field.
Tutorial #12   []	Handout   Solutions
gamma^5 matrix and Left/Right-chiral fields. Weyl fields (and problem of coupling by mass). Transformation properties of vectors/axial vectors.
Tutorial #13   []	Solutions
Massive vector bosons (the Proca equation). Propagating degrees of freedom for spin-1 fields. EoM for the Yang-Mills Lagrangian. SU(2) charges of weak interactions.
Tutorial #14   []	Handout   Solutions
Higgs mechanism: generation of mass for Z bosons and photons, Higgs decays Suggested reading: Schwartz ch 29.1-29.2, Mandl and Shaw chapter 18-19 Additional notes on spontaneous symmetry breaking
Tutorial #15   []	Solutions
Path Integrals. Preliminaries. Gaussian integrals. Grassmann numbers
Tutorial #16   []	Solutions
Path Integrals, Part II. Perturbation expansion for the phi^4-theory.
Tutorial #17   []
Old exam problems.