Quantum Field Theory (FK8017)
Course Information for 2016/2017
1. The fourth homework problem set is available below.
The deadline for submitting the solutions is Friday, March 03, 2017
Text BookCourse Book: "Quantum Field Theory" by F. Mandl and G. Shaw (Second Edition from 2010)
TutorialsDetailed information about tutorial sessions can be found here . Please use this page to decide on the dates for tutorial sessions.
Some Lecture NotesThese notes are meant to supplement the book.
Homework ProblemsProblem set 1 (due date: Nov 24, 2016)
Problem set 2 (due date: Dec 19, 2016)
Problem set 3 (due date: Feb 06, 2017)
Problem set 4 (due date: March 03, 2017)
Examples of classical fields and field equations. Review of
analytical mechanics of particles, Poisson brackets and
quantization. Lagrangian and Hamiltonian formulations of classical
field theory, the Euler-Lagrange equation. Lorentz
transformations and SO(1,3), classical theories of scalar, vector
and spinor fields.
Symmetries and conservation laws in field theory (proof and applications of Noether's theorem). Spacetime and global gauge symmetries. The energy-momentum tensor, conservation of charge, energy, momentum, angular momentum and spin.
Quantization of relativistic free fields: Real and complex scalar fields, conserved quantities, particle interpretation. The electromagnetic field, guage invariance and gauge fixing, the Gupta-Bleuler quantization. The Dirac field, spinors as SO(1,3) representations, conserved quantities. Normal ordering, Causality and the spin-statistics relation. The Feynman propagator and its contour integral representation.
Interactions from local gauge invariance: the Abelian case, electrodynamics. Interacting fields in QFT: the interaction picture, S-matrix and its expansion in perturbation theory, Wick's theorem. Application to Quantum Electrodynamics (QED), Feynman rules and the Feynman amplitude, the scattering cross-section, sum over spins and polarizations. Calculation of cross sections in Bhabha, Möller and Compton scatterings, etc.
Non-Abelian gauge theories (with a review of basic group theory, and Lie algebras, SU(n) groups). The basics of Quantum Chromodynamics (QCD) as the theory of strong interactions.
Introduction to (leptonic) Weak interactions, chiral fermions, massive vector fields, the V-A structure. Weak interactions as an SU(2)xU(1) gauge theory, identification of electromagnetism. Spontaneous symmetry breaking, Goldstone and Higgs mechanisms. Higgs mechanism in SU(2)xU(1) gauge theory, Yukawa couplings and fermion masses. The mass matrix and neutrino mixings. Theory of electroweak interactions and the standrd model of particle physics.
Path integral formulation of quantum field theory. Functional integrals for bosonic and fermionic fields. Interactions in the PI formulation. The generating function and perturbative expansions. Path integral quantization of Abelian and non-Abelian gauge theories, gauge fixing the and Faddeev-Popov procedure, the Faddeev-Popov ghosts.
Radiative corrections: regularization, renormalization, calculation of Lamb-shift and anomalous magnetic moment.