Tutorials (done)

Tutorial #1 (mk 2017-10-30) Handout   Solutions
Notation, Lorentz invariance, Index gymnastics, Dirac delta function.

Tutorial #2 (ft 2017-11-06) Handout   Notes
Natural Units and Dimensional Analysis. SR recap II.

Tutorial #3 (mk 2017-11-13) Handout   Fields overview   Solutions
More on SR. Fourier Transform. The Lagrangian of the real scalar (KGF) field. Harmonic oscillator, ladder operators. Heisenberg algebra.

Tutorial #4 (ft 2017-11-20) Notes
Ladder operators and Heisenberg algebra (contd). 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 2017-11-27) Handout   Part 1   Part 2
(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. (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.)

Tutorial #6 (mk 2017-12-04) Handout   Solutions   Overview
contd. Part II ( The expansion of the Hamiltonian)
Symmetries and Conservation Laws. Noether’s theorem. (Additional references: Chapter 8 from Hagen Kleinert's Book on Particles and Quantum Fields)

Tutorial #7 (ft 2017-12-11) Handout I   Handout II   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 (mk 2017-12-18)
Dirac field and gamma matrices (contd). Maxwell field, gauge fixing. Highlights from Problem Set 1.

Tutorial #9 (mk 2018-01-08) 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 2018-01-15) Solutions Notes
Problems 7.1, 7.3 and 7.5 (Mandl & Shaw), Feynman amplitudes for QED.

Tutorial #11 (ft 2018-01-22) Handout Solutions
Additional notes: On the relativistic definition of flux and the invariant cross-section

Tutorial #12 (mk 2018-01-29) Handout Solutions
gamma^5 matrix and Left/Right-chiral fields. Weyl fields (and problem of coupling by mass). Transformation properties of vectors/axial vectors. Massive vector bosons (the Proca equation). EoM for the Yang-Mills Lagrangian. SU(2) charges of weak interactions.

Tutorial #13 (ft 2018-02-12) Solutions
Weak Interactions.

Tutorial #14 (ft 2018-02-19) 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 2018-02-26) Solutions
Path Integrals. Preliminaries. Gaussian integrals. Grassmann numbers

Tutorial #16 (mk 2018-03-05) Solutions
Path Integrals, Part II. Perturbation expansion for the phi^4-theory.