Symmetries and Quantum Field Theory - Département de Physique de l'Ecole Normale supérieure

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Symmetries and Quantum Field Theory

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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
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November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty: Matthieu TISSIER

Tutor: Julien SERREAU

ECTS credits: 6

Language of instruction: English

Examination: Written

Course description

This is an introductory course to quantum field theory, a formalism that is needed to describe elementary particles and their interactions, together with a large class of condensed matter systems. In a first part, classical field theory with relativistic invariance is introduced. Particular emphasis is put, on the one hand, on the relationship between symmetries, and on the other, on the nature of possible particles and their dynamics. As a consequence of this approach, the scalar field, the vectorial field and the spinorial field appear naturally. Their transformation properties under the action of the Lorentz group are thoroughly exposed. The dynamical equations obeyed by those fields are presented, and motivated (Klein-Gordon, Maxwell and Dirac equations). Low energy applications in condensed matter (as e.g. graphene, or topological insulators) are discussed. In the second part of this course, the free fields are quantized. The Fock space, and its interpretation in terms of particles, is introduced. Finally, the course ends up with an introduction to the concept of spontaneous symmetry breaking in quantum field theory. In particular, the two viewpoints on symmetries in quantum field theory (Wigner-Weyl and Nambu-Goldstone) are introduced, and the Goldstone theorem is proved.

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr