Tutorials (done)

Tutorial #1   [mk]   2018-11-05 Handout   Solutions
Notation, Lorentz invariance, Index gymnastics, Dirac delta function.

Tutorial #2   [ft]   2018-11-12 Handout / Notes 1, Notes 2
Natural Units and Dimensional Analysis. SR recap II. Ladder operators and Heisenberg algebra.

Tutorial #3   [mk]   2018-11-19 Handout   Fields overview   Solutions
Fourier Transform. The Lagrangian of the real scalar (KGF) field.

Tutorial #4   [ft]   2018-11-26 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   [mk]   2018-11-28 Handout   Part 1  
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   [mk]   2018-12-10 Handout  
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   [ft]   2018-12-17 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   [ft]/[mk]   moved to 2018-12-17
Dirac field and gamma matrices (contd).
Maxwell field, gauge fixing. Highlights from Problem Set 1.

Tutorial #9   [mk]   moved to 2018-12-19) 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   [ft]   2019-01-21 Solutions, Feynman diagrams
Problems 7.1, 7.3 and 7.5 (Mandl & Shaw), Feynman amplitudes for QED.

Tutorial #11   [ft]   2019-01-28) Handout Solutions
Cross-sections. The relativistic definition of flux. The spin-sums lemma. The e-e+ production in electromagnetic field.

Tutorial #12   [mk]   2019-02-04) 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   [ft]   2019-02-11 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   [ft]   2019-02-18 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   [mk]   2019-02-25
Path Integrals. Preliminaries. Gaussian integrals. Grassmann numbers

Tutorial #16   [mk]   2019-03-04
Path Integrals, Part II. Perturbation expansion for the phi^4-theory.

Tutorial #17   [ft]   2019-03-11
Old exam problems.