Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes, starting from a careful definition of symmetry in physics, we introduce symmetry breaking and its consequences. Emphasis is placed on the physics of singular limits, showing the reality of symmetry breaking even in small-sized systems. Topics covered include Nambu-Goldstone modes, quantum corrections, phase transitions, topological defects and gauge fields. We provide many examples from both high energy and condensed matter physics. These notes are suitable for graduate students.
Cited by 2
Louk Rademaker et al., Stability and absence of a tower of states in ferrimagnets
Phys. Rev. Research 2, 013304 (2020) [Crossref]
Christiaan J. F. van de Ven et al., Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking
SciPost Phys. 8, 022 (2020) [Crossref]
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- 1 Keio University
- 2 Université de Genève / University of Geneva [UNIGE]
- 3 Perimeter Institute [PI]
- 4 Institute of Physics, University of Amsterdam [IoP, UvA]
- Gouvernement du Canada / Government of Canada
- 日本学術振興会 / Japan Society for the Promotion of Science [JSPS]
- 文部科学省 Monbu-kagaku-shō / Ministry of Education, Culture, Sports, Science and Technology [MEXT]
- Ministry of Research and Innovation (Canada, Ontario, Min Res&Innov) (through Organization: Ministry of Research, Innovation and Science - Ontario [MRIS])
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung / Swiss National Science Foundation [SNF]