This site contains the notes for the QFT tutorial sessions

You can reach us at:
Mikica: mikica.kocic (at) fysik.su.se, Room: A5:1031 -- Meeting request: Doodle
Francesco: francesco.torsello (at) fysik.su.se, Room: A5:1031

Mindmaps

Tutorials (scheduled)

Tutorial #1 Handout
Notation, Lorentz invariance, Index gymnastics, Dirac delta function.

Tutorial #2 Handout
Tutorial on index gymnastics. (The notes hare are for the last year's tutorail on: Natural Units and Dimensional Analysis. Harmonic oscillator, ladder operators. Heisenberg algebra.)

Tutorial #3 Handout
The Lagrangian of the real scalar (KGF) field. 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 #4 Handout
The expansion of the Hamiltonian. An introduction to the infinite contributions to the energy and the normal ordering of operators.

Tutorial #5 Handout
Topic on symmetries.

Tutorial #6 Part I: Handout, Part II: Handout
Part I. Gamma matrices, Dirac algebra. Part II. The Dirac field.

Tutorials #7 Handout
The Dirac field. (continued)

Tutorials #8 Handout
The Schrödinger, Heisenberg and Interaction Pictures.
Perturbation Expansion of the S-Matrix.

Tutorials #9 Handout
Perturbation Expansion of the S-Matrix. (continued)
Wick’s Theorem. QED processes at 2nd order.
Additional references:
The Schrodinger, Heisenberg and Interaction Pictures in QFT
Invariant commutation and propagation functions
Overview of the fields in QFT

Tutorial #10
Problems 7.1, 7.3 and 7.5 (Mandl & Shaw), Feynman amplitudes for QED.

Tutorial #11 Handout
Cross-sections.

Tutorial #12 Handout
gamma^5 matrix and Left/Right-chiral fields. Weyl fields (and problem of coupling by mass). Transformation properties of vectors/axial vectors. EoM for the Yang-Mills Lagrangian. SU(2) charges of weak interactions.

Tutorial #13
Massive vector bosons (the Proca equation). Weak Interactions.

Tutorial #14 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

Tutorial #15
Path Integrals. Preliminaries. Gaussian integrals. Grassmann numbers

Tutorial #16
Path Integrals, Part II. Perturbation expansion for the phi^4-theory.

Tutorial #17 Handout
Some old exam problems.

Useful external resources

Useful external resources


Tutorial Plan

Textbook: Mandl, Franz and Shaw, Graham - Quantum Field Theory (2nd ed., 2010),
ISBN: 9780471496830

Chapters in Mandl and Shaw
2 Lagrangian field theory
3 Klein-Gordon field
4 Dirac field
5 Photons
6 S-matrix expansion
7 Feynman diagrams
8 QED at lowest order
(9)(Radiative corrections)
(10)(Regularization)
11 Gauge theories
13 Path integrals
(14)(QCD)
(15)(Asymptotic freedom)
16 Weak interactions
17 Gauge theory of weak interactions
18 Spontaneous symmetry breaking
19 Standard electro-weak theory
Chapters in Schwartz
2 Lorentz transformations
5 Cross-sections
10 Spinors and Dirac equations
Additional topics
Group theory(join with Schwartz, Ch 2)
Heisenberg algebra (ladder operators)(join with KG-field)

Note: Four chapters in parentheses (9, 10, 14 & 15) — if there is time.

Supplementary reading:

  • "Classical Mechanics" by H. Goldstein, C. P. Poole, J. L. Safko (chapter 13)
  • "Quantum Theory and the Standard Model" by Matthew D. Schwartz (Cambridge University Press)
  • "Quantum Field Theory" by Mark Srednicki. (You can try a prepublication draft of this book on the author's webpage here. Note that the author follows different signature convention for the metric than one usually used in Mandl and Shaw.)
  • Another book for path integrals in QFT is "Field Theory: A Modern Primer" by Pierre Ramond, section 3.1, 3.2, 4.1.