This site contains the notes for the QFT tutorial sessions

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


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

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)
11 Gauge theories
13 Path integrals
(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.