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.
• Give constructive criticism on the quality and progress of a project.
• Work in teams and, in particular, communicate effectively and with respect for others.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• Communicate clearly.
• Communicate the results of mathematical or related fields, both orally and in writing, by adapting to the public.
• make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.
• Have sufficient knowledge of English for basic scientific communication.
• Skill 6: Have acquired professional skills in relation to the objective defining the degree.
• Have gained expertise and specialised knowledge in a field of mathematics in order to enter fully into the world of research.
• Demonstrate intuition and creativity to tackle new mathematical problems.
• Expose high-level mathematical results to a specialised audience.
• 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.
• Research mathematical literature in an efficient and relevant way.
• Read research articles in at least one discipline of 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.
• Give constructive criticism on the quality and progress of a project.
• Work in teams and, in particular, communicate effectively and with respect for others.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• 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.
• Give constructive criticism on the quality and progress of a project.
• Work in teams and, in particular, communicate effectively and with respect for others.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• Communicate clearly.
• Communicate the results of mathematical or related fields, both orally and in writing, by adapting to the public.
• make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.
• Have sufficient knowledge of English for basic scientific communication.
• Adapt to different contexts.
• Have developed a high degree of independence to acquire additional knowledge and new skills to evolve in different contexts.
• Critically reflect on the impact of mathematics and the implications of projects to which they contribute.
• Demonstrate thoroughness, independence, creativity, intellectual honesty, and ethical values.

Learning Outcomes of UE

By the end of the course, the student should know the path-integral formulation of quantum mechanics and quantum field theory. He/she should know the 1-loop renormalisation of Quantum Electro-Dynamics (QED), the Ward-Takahashi identities and the Becchi-Rouet-Stora-Tyutin (BRST) transformations in QED. The student should know the basics of renormalisation group and beta function.

Content of UE

Teaching in English.
Path integral formulation of quantum mechanics and quantum field theory. Definition, gaussian approximation. Quantum Electro-Dynamics (QED). Feynmann diagrams in QED. Classification of the divergent diagrams at one loop. Regularisation and renormalisation. Renormalisation group, beta function. Dimensional regularisation.

Prior Experience

Quantum Field Theory I

Type of Assessment for UE in Q2

• Presentation and/or works
• Oral Examination

Q2 UE Assessment Comments

None

Type of Assessment for UE in Q3

• Presentation and/or works
• Oral examination

Q3 UE Assessment Comments

None