An introduction to Quantum Field Theory I by J. Zinn-Justin, CEA/IRFU
Sommaire des cours
1. October 29th, 2015:
(a) Random walk, continuum limit, Brownian motion and Gaussian path integral.
(b) The role of path and field integrals in modern physics
2. November 5th, 2015:
Quantum mechanics: path integral representation of the evolution operator and matrix density at thermal equilibrium. The example of the quantum harmonic oscillator. Perturbation theory and Wick’s theorem. Euclidean or imaginary time formalism: Barrier penetration in the semi-classical limit.
A technical problem has prevented the registration of the lecture; sorry.
3. November 19th, 2015:
From particles to fields. The holomorphic formalism: From the harmonic oscillator to the quantum Bose gas.
4. November 26th, 2015:
The scalar field. Free field. Generating functional. Perturbative expansion and Wick’s theorem in field theory. Loop expansion. The problem of infinities. Regularization. Renormalization. The problem of fine tuning. Renormalization group equations. The problem of triviality. A bound on the Higgs mass.
A technical problem has prevented the registration of the lecture; sorry.
5. December 3rd, 2015:
The scalar field: Spontaneous symmetry breaking. Goldstone bosons. Ward-Takahashi identities and renormalization.
6. December 10th, 2015:
Path integrals and fermions: Grassmann algebra, differentiation and integration. Path integrals. Wick’s theorem. The non-relativistic Fermi gas.
7. December 17th, 2015:
The Dirac fermion. Free field. Perturbative expansion. Regularization and renormalization of a Yukawa-type field theory. The non-relativistic limit. The Gross-Neveu-Yukawa model: a toy model for Higgs-top interaction.
8. Notions sur symétries et transitions de phases: la théorie de Landau:
symetrie12.pdf
Session 2:
9. February 04th, 2016:
Dimensional continuation: Application to critical phenomena
10. February 11th, 2016:
Fermions in the grassmann formalism
11. February 18th, 2016:
From non-relativistic to relativistic fermions in the grassmann formalism
12. March 24th, 2016:
Symmetries and symmetry breaking
13. March 31th, 2016:
Abelian gauge theories: the framework of QED
14. April 21th, 2016:
Non-abelian gauge theories: the basis of the standard model
15. May 19th, 2016:
The standard model. Anomalies
16. May 26th, 2016:
Lattice gauge theories: an introduction
