Objectives of Programme's Learning Outcomes

• Have integrated and elaborate mathematical knowledge.
• Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
• Use prior knowledge to independently learn high-level mathematics.
• Carry out major projects.
• Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.
• Apply innovative methods to solve an unprecedented problem in mathematics or within its applications.
• Mobilise knowledge, and research and analyse various information sources to propose innovative solutions targeted unprecedented issues.
• Carry out major projects.
• Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.

Learning Outcomes of UE

Improve our understanding of space time. Show how group representations can help in constructing relativistic equations. Show how it predicts anti-matter. Show how equations can be formulated in terms of variational calulations. Introduce the notion of quantum field theory and its pertubative treatment. Compute tree level Feynmann diagrams

Content of UE

 Lorentz and  Poincaré groups. Representations of these groups. Construction of relativistic covariant equations. Klein-Gordon and Dirac equations. Relativistic Hydrogen atom. Charge conjugaison. Lagrangian approach and Euler-Lagrange equations. Noether theorem Canonical quantization of the Klein-Gordon, Dirac and Maxwell fields. Propagator, Wiick theorem. Perturbative approach of quantum field theory. Feynmann rules for quantum electrodynamics

Prior Experience

Concept of special relativity and of quantum mechanics

Type of Assessment for UE in Q1

• Written examination

Q1 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

• Written examination

Q3 UE Assessment Comments

Not applicable

Type of Resit Assessment for UE in Q1 (BAB1)

• Written examination

Q1 UE Resit Assessment Comments (BAB1)

Not applicable