**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

- Teaching coordinator: Kopper Christoph
- Teaching coordinator: Lorcé Cédric