Relativistic fields and their quantization

We give an introduction to the theory of relativistic quantum fields which is at the basis of elementary particle theory :

  • Reminder of notions from quantum mechanics and relativity.
  • The Klein-Gordon equation.
  • The Dirac equation.
  • Relativistic covariance of the Dirac equation. Parity and charge conjugation.
  • Lagrangian field theory. Lagrangian, Euler-Lagrange equations, Hamiltonian, energy-momentum tensor and Noether current.
  • Quantisation of the scalar field. Hamiltonian, creators and annihilators, Hilbert space, vacuum energy.
  • Quantisation of the electromagnetic field. Lagrangian, energy and momentum, mode decomposition and polarisation. Massive vector field. Abelian Brout-Englert-Higgs mechanism.
  • Quantisation of the Dirac field. Lagrangian, Hamiltonian, anticommutation relations. Charge conjugation. Vacuum energy for fermions and bosons.
  • A survey of the electroweak and Higgs sectors of the standard model. Neutral and charged electroweak currents.
  • Decay rates of the W et Z bosons: A first-order quantum field theory calculation.


Required level:
PHY431 - Relativity and variational principles
PHY430 - Advanced quantum physics
PHY433 - Statistical physics

Course language: English