Study programme 20232024  Français  
Théorie quantique des champs I  
Programme component of Master's in Mathematics : Research Focus (MONS) (day schedule) à la Faculty of Science 
Code  Type  Head of UE  Department’s contact details  Teacher(s) 

USM2MATHFA015M  Optional UE  BOULANGER Nicolas  S827  Physique de l'Univers, Champs et Gravitation 

Language of instruction  Language of assessment  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Credits  Weighting  Term 

 Français  30  20  0  0  0  9  9.00  1st term 
AA Code  Teaching Activity (AA)  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Term  Weighting 

SPHYS049  quantum field theory I  30  20  0  0  0  Q1  100.00% 
Programme component 

Objectives of Programme's Learning Outcomes
Learning Outcomes of UE
By the end of the course, the student should know the very basics of Relativistic Quantum Field Theory in flat spacetime. In particular, he/she should be able to identify the relevance of the Poincaré and its unitary irreducible representations for the classification of linear relativistic wave equations in flat spacetime. The student should be able to derive the various fundamental relativistic field equations (KleinGordon, Dirac, Maxwell, Fronsdal) from a corresponding variational principle. He/she should be able to apply Noether's theorem for relativistic field theories in order to construct conserved current densities. The student should know our to canonically quantize a free field of arbitrary spin. In particular, how to deal with gauge invariance for the quantization of Maxwell's vector field. He/she should be able to compute the scattering S matrix in timedependent perturbation theory and explicitly compute some Feynman diagrams at tree level for simple scattering processes in Quantum Electrodynamics.
UE Content: description and pedagogical relevance
Lorentz and Poincaré groups. Classification of the unitary irreducible representations of the Poincaré group. Variational principles in Relativistic Field Theory: KleinGordon, Dirac, Maxwell, FierzPauli and Fronsdal field equations. Gauge invariances and rigid symmetries. Relativistic Hydrogen atom. Noether theorem in Field Theory. Canonical quantization of free fields of spin less than two. Method of Dirac for constained systems. Propagators, Wick theorem. Timedependent perturbation theory for the scattering S matrix. Reduction formula. Feynmann rules for quantum electrodynamics.
Prior Experience
Classical electrodynamics, analytical mechanics, quantum mechanics, group theory, special relativity and complex analysis.
Type of Teaching Activity/Activities
AA  Type of Teaching Activity/Activities 

SPHYS049 

Mode of delivery
AA  Mode of delivery 

SPHYS049 

Required Learning Resources/Tools
AA  Required Learning Resources/Tools 

SPHYS049  Lectures given at the blackboard, lecture notes on Teams. 
Recommended Learning Resources/Tools
AA  Recommended Learning Resources/Tools 

SPHYS049  M. Srednicki, Quantum Field Theory, CUP S. Weinberg, The Quantum Theory of Fields. 1, CUP 
Other Recommended Reading
AA  Other Recommended Reading 

SPHYS049  L.H. Ryder, Quantum Field Theory, 2nd edition, 508 pp., Cambridge U.P. (1996) 
Grade Deferrals of AAs from one year to the next
AA  Grade Deferrals of AAs from one year to the next 

SPHYS049  Authorized 
Term 1 Assessment  type
AA  Type(s) and mode(s) of Q1 assessment 

SPHYS049 

Term 1 Assessment  comments
AA  Term 1 Assessment  comments 

SPHYS049  At the written part of the exam, the student will have to solve some short problems. At the oral examination, questions will be asked about the whole content of the course. The student will have to use the blackboard to answer the questions. 
Resit Assessment  Term 1 (B1BA1)  type
AA  Type(s) and mode(s) of Q1 resit assessment (BAB1) 

SPHYS049 

Term 3 Assessment  type
AA  Type(s) and mode(s) of Q3 assessment 

SPHYS049 

Term 3 Assessment  comments
AA  Term 3 Assessment  comments 

SPHYS049  Same examination mode as in January. 