Study programme 2019-2020Français
Théorie quantique des champs I
Programme component of Master's in Mathematics : Research Focus à la Faculty of Science

Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what assessment methods are planned for the end of Q3

CodeTypeHead of UE Department’s
contact details
Teacher(s)
US-M2-MATHFA-015-MOptional UEBOULANGER NicolasS827 - Physique de l'Univers, Champs et Gravitation
  • BOULANGER Nicolas

Language
of instruction
Language
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français
Français302000099.001st term

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-PHYS-049quantum field theory I3020000Q1100.00%
Programme component

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.
    • Work in teams and, in particular, communicate effectively and with respect for others.
  • 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.
  • 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.
    • Work in teams and, in particular, communicate effectively and with respect for others.
  • Carry out major projects.
    • Work in teams and, in particular, communicate effectively and with respect for others.
  • 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 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 (Klein-Gordon, 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 time-dependent perturbation theory and explicitly compute some Feynman diagrams at tree level for simple scattering processes in Quantum Electrodynamics.

Content of UE

Lorentz and  Poincaré groups. Classification of the unitary irreducible representations of the Poincaré group. Variational principles in Relativistic Field Theory: Klein-Gordon, Dirac, Maxwell, Fierz-Pauli 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. Time-dependent 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 Assessment for UE in Q1

  • Oral examination
  • Written examination

Q1 UE Assessment Comments

At the exam, the student will have to solve a problem and present the solution on the blackboard. During the presentation and after it, questions will be asked about the whole content of the course.

Type of Assessment for UE in Q3

  • Oral examination
  • Written examination

Q3 UE Assessment Comments

Same examination mode as in January

Type of Resit Assessment for UE in Q1 (BAB1)

  • N/A

Q1 UE Resit Assessment Comments (BAB1)

Not applicable

Type of Teaching Activity/Activities

AAType of Teaching Activity/Activities
S-PHYS-049
  • Cours magistraux
  • Exercices dirigés

Mode of delivery

AAMode of delivery
S-PHYS-049
  • Face to face

Required Reading

AA
S-PHYS-049

Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-PHYS-049Lectures given at the blackboard.

Recommended Reading

AA
S-PHYS-049

Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-PHYS-049None

Other Recommended Reading

AAOther Recommended Reading
S-PHYS-049L.H. Ryder, Quantum Field Theory, 2nd edition, 508 pp., Cambridge U.P. (1996)

Grade Deferrals of AAs from one year to the next

AAGrade Deferrals of AAs from one year to the next
S-PHYS-049Authorized
(*) HT : Hours of theory - HTPE : Hours of in-class exercices - HTPS : hours of practical work - HD : HMiscellaneous time - HR : Hours of remedial classes. - Per. (Period), Y=Year, Q1=1st term et Q2=2nd term
Date de génération : 13/07/2020
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Courriel: info.mons@umons.ac.be