# Tutorials (done)

 Tutorial #1   [Jo]   2018-11-11 Handout   Solutions Notation, Lorentz invariance, Index gymnastics, Dirac delta function. Tutorial #2   [Fr]   2018-11-13 Handout   Notes   Solutions Natural Units and Dimensional Analysis. SR recap II. Ladder operators and Heisenberg algebra. Tutorial #3   [Jo]   2018-11-18 Handout   Fields overview   Solutions Fourier Transform. The Lagrangian of the real scalar (KGF) field. Tutorial #4   [Fr]   2018-11-25 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   [Ju]   2018-12-02 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   [Fr]   2018-12-09 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   [Fr]   2018-12-16 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.

# Tutorials (scheduled)

 Tutorial #8   [Fr,Ju]   2019-01-08 Dirac field and gamma matrices (contd). Maxwell field, gauge fixing. Highlights from Problem Set 1. Tutorial #9   [Ju]   2019-01-13 Handout 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   [Fr]   2019-01-20 Problems 7.1, 7.3 and 7.5 (Mandl & Shaw), Feynman amplitudes for QED. Tutorial #11   [Fr]   2019-01-27) Handout Cross-sections. The relativistic definition of flux. The spin-sums lemma. The e-e+ production in electromagnetic field. Tutorial #12   [Jo]   2019-02-03) Handout gamma^5 matrix and Left/Right-chiral fields. Weyl fields (and problem of coupling by mass). Transformation properties of vectors/axial vectors. Tutorial #13   [Fr]   2019-02-10 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   [Fr]   2019-02-17 Handout 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   [Jo]   2019-02-24 Path Integrals. Preliminaries. Gaussian integrals. Grassmann numbers Tutorial #16   [Jo]   2019-03-02 Path Integrals, Part II. Perturbation expansion for the phi^4-theory. Tutorial #17   [Fr]   2019-03-09 Old exam problems.