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

ECTS credits: 5