Objectifs :
1. Define and classify symmetries in physical theories, distinguishing between global and local, continuous and discrete symmetries.
2. Explain the concept of spontaneous symmetry breaking (SSB) and its physical significance, including the emergence of collective modes (e.g., Nambu–Goldstone bosons) and the impact of quantum corrections on symmetry-breaking phenomena.
3. Analyze the phenomenology of phase transitions and symmetry-breaking patterns, including the classification of topological defects (domain walls, vortices, monopoles) and the interaction with gauge fields (e.g., the Higgs mechanism and its condensed matter analogues).
4. Apply the theoretical framework to a broad range of examples from high energy and condensed matter physics, and critically assess the role of symmetry and its breaking in the emergence of effective theories and collective behavior.

Programme :
1. Symmetries in Physics: Definitions and Classifications
Global and local symmetries, continuous and discrete symmetries, Noether’s theorem, conserved quantities.
2. Spontaneous Symmetry Breaking (SSB)
Quantum aspects of SSB, thermodynamic limit, Nambu–Goldstone theorem, emergence of collective modes, quantum corrections.
3. Phase Transitions and Critical Phenomena
Landau theory of phase transitions, order parameters, first- and second-order transitions, universality, critical behavior.
4. Gauge Symmetry
Spontaneous breaking of gauge symmetry, the Higgs mechanism, gauge boson masses, connections with condensed matter and particle physics.

Pré-requis :
Good knowledge of quantum field theory and basic knowledge of physical phenomena in condensed matter and/or particle physics

Equipe pédagogique :
Flavio RONETTI (CPT)

Méthode pédagogique :
The course combines formal lectures with interactive discussions and problem-solving sessions. Emphasis is placed on conceptual understanding, physical intuition, and the ability to apply theoretical tools to concrete examples. Students are encouraged to actively engage with the material through guided exercises and presentations of key topics or applications. Connections between high energy and condensed matter physics are highlighted throughout, fostering a unified view of symmetry breaking across disciplines.

Compétences acquises à l'issue de la formation :
1. Understand and analyze the role of symmetry and spontaneous symmetry breaking in quantum physical systems.
2. Apply key theoretical tools—such as the Nambu–Goldstone theorem, effective potentials, and gauge symmetry breaking (including the Higgs mechanism)—to problems in both condensed matter and particle physics.
3. Develop a cross-disciplinary perspective on emergent phenomena, recognizing how symmetry breaking shapes the behavior of complex physical systems across different domains.

La formation participe à l'objectif suivant :conforter la culture scientifique des doctorants dans leur champ disciplinaire ou en interdisciplinaire