UE Quantum field theory I



- Chapter 1 helps prepare students for the canonical quantisation of the scalar field through a review of phonons, and for a classical then quantum study of the continuous line followed by acoustic waves.

- Chapter 2 is devoted to the different fields involved in quantum electrodynamics that will be quantised according to the canonical approach. We will begin with a study of the Klein-Gordon scalar field or spin 0 neutral field. We will first examine the classical derivation of the equations verified by this field, and construct its energy-momentum tensor using Noether's theorem. This will be followed by a study of the canonical quantisation of the neutral scalar field and the construction of Hamiltonian and momentum operators.

- We will then move onto the charged scalar field as a way of describing pions. A new conserved quantity is obtained. This is the electric charge in the case of the electromagnetism and the associated invariance under U(1), but any other quantum charge may be introduced. We will then focus on the Feynman propagator of the charged scalar field as well as the associated T-product.

- We will quantify the electromagnetic field, whose classical properties will have already been studied. Maxwell equations and gauge invariances. Lagrangian formalism and energy-momentum tensor. Lastly, Gupta-Bleuler quantisation will be presented.

- The chapter will finish with quantisation of the fermion field with half-integer spin represented by the electrons and their antiparticles the positrons. A review of the Dirac equation will probably be necessary. Lagrangian analysis and energy-momentum tensor. Then a second quantisation and derivation of the anticommutation relations that reflect the fact that a half-integer spin particle is a fermion. We will conclude with the Feynman propagator of the electron, which has already been presented in the Relativistic Quantum Mechanics course of Semester 8.


skin.odf-2017:SKIN_ODF_CONTENT_COURSE_INFOS_LIEUX_TITLEGrenoble - Domaine universitaire