PHYS-431 Quantum field theory I

1. Introduction: Fundamental motivations for quantum field theory,
Natural units of measure, Overview of particle physics.

2. Classical Field Theory: Lagrangian and Hamiltonian formulation.

3. Symmetry Principles: Elements of group theory, Lie groups, Lie Algebras, group representations,
Lorentz and Poincaré groups.

4. Irreducible representations of the Poincaré group.

5. Noether theorem: conserved currents, conserved charges, the conserved charges of the Poincarè group and their interpretation.

7. Canonical quantization of  real and complex scalar fields.  Creation and annihilation operators. Fock space. Bose statistic. Heisenberg picture field. Realization of symmetries in the quantum theory.

6. Spinorial representations of the Lorentz group. Weyl, Majorana and Dirac spinors and their wave equations. Quantization of the Dirac field. Anticommutation relations and Fermi statistics. Spin.

8. Causality in QFT.

Required prior knowledge: Electrodynamics, Special relativity, Quantum Mechanics I and II.

Teaching: Ex cathedra (3 hrs per week, 14 weeks) and exercises (2hrs per week, 14 weeks)

Exam: oral, consisting of one theoretical question and one exercise, picked randomly and for which the candidate is allowed a 30 minute preparation

Note: Prerequisite for Theoretical Physics