UE Quantum field theory II



- Until now, the quantum fields studied have been free. In Chapter 3, we will now create interactions between them, with firstly a review of perturbation theory and the S-matrix. Schroedinger and Heisenberg pictures, and free Hamiltonian H0. General case and U evolution operator. Interaction picture and S-matrix.

- Continuation of Chapter III devoted to the study of Wick's theorem. Demonstration in the purely bosonic case, then the purely fermionic case, finishing with the general case.

- We will conclude by establishing the Feynman rules through a calculation of the cross-section of a simple process. Writing the S-matrix element. Determination of Sfi and Feynman rules of quantum electrodynamics. Differential cross-section. We will develop the method for the general calculation of Feynman rules from an interaction Lagrangian.

- Chapter IV will be devoted to a study of the Yang-Mills theories from a classical perspective. We will initially return to the concept of covariant derivative in electromagnetism, which will be used to introduce non-abelian gauge theories. Gauge rotation on a field multiplet. Covariant derivative Dμ and vector potential Aμ.

- The next session will be devoted to gauge fields and their properties. These fields are represented by the photon in the case of electrodynamics, and by gluons in quantum chromodynamics.

- The concept of spontaneous symmetry breaking will be introduced and studied, first in the teaching example of the Mexican hat, and then generalised to the SO(n) and SU(2) groups.

- Goldstone's theorem will be demonstrated in the general case. This part is slightly esoteric. Then, the Higgs miracle will be studied. This mechanism will be illustrated in a simple case and then generalised to the SU(2) group.

- We will then be ready to understand the Weinberg-Salam model for unifying weak and electromagnetic interactions. After building the Lagrangian, we will analyse the spontaneous breaking of the SU(2)L × U(1)Y group and determine the masses of the W± and Z0 vector bosons according to the vacuum value of the Higgs field. Calculation of the fermion and gauge-boson couplings. Study of the Higgs sector and Yukawa couplings.


skin.odf-2017:SKIN_ODF_CONTENT_COURSE_INFOS_LIEUX_TITLEGrenoble - Domaine universitaire