All lecture notes in one pdf file: lectures_Brauner.pdf.

This page collects basic information and materials for the lecture series on Spontaneous symmetry breaking and Nambu-Goldstone bosons at the 28^th Saalburg Summer School. For any inquiries, send an e-mail to tomas.brauner@uis.no. The series consists of four lecture blocks with the following tentative outline:

Lecture 1.
- Outline: symmetry of dynamics and of physical states; spontaneous symmetry breaking (SSB) and the thermodynamic limit; fluctuations of the order parameter; Goldstone theorem; classification of Nambu-Goldstone (NG) bosons.
- Lecture notes: lecture1.pdf
- Exercise sheet: exercise1.pdf, exercise1_solution.pdf
- Further reading:
  - Beekman_Rademaker_Wezel.pdf: large amount of background on both SSB and NG bosons.
  - Naegels.pdf: general background on SSB and NG bosons (secs. 1-3).
  - Watanabe.pdf: classification of NG bosons.

Lecture 2.
- Outline: need for low-energy effective field theory (EFT) of NG bosons; action of groups on manifolds; coset space of broken symmetry; nonlinear realization of symmetry on the coset space; symmetric coset spaces.
- Lecture notes: lecture2.pdf
- Exercise sheet: exercise2.pdf, exercise2_solution.pdf
- Further reading:
  - Penco.pdf: general background on EFT.
  - Naegels.pdf: introduction to the coset construction (sec. 4.1).
  - TB_coset_construction.pdf: private notes on the coset construction.
Lecture 3.
- Outline: background gauge invariance; gauged Maurer-Cartan form; invariant and quasi-invariant effective Lagrangians; general leading-order effective action; low-energy EFT for ferromagnets.
- Lecture notes: lecture3.pdf
- Exercise sheet: exercise3.pdf, exercise3_solution.pdf
- Further reading:
  - Andersen_et_al.pdf: detailed account of the background gauge invariance approach to EFT for NG bosons.
  - TB_ferromagnet.pdf: private notes on EFT for ferromagnets.
  - Watanabe_Murayama.pdf: tour de force construction of EFT for NG bosons with everything you ever wanted to know and more.
Lecture 4.
- Outline: Adler zero property; scattering amplitudes from the geometry of coset space; selected topological aspects of SSB; no-go theorems for SSB; classification of NG bosons and coset construction for spontaneouly broken spacetime symmetries.
- Lecture notes: lecture4.pdf
- Exercise sheet: exercise4.pdf
- Further reading:
  - Cheung_Helset_Parra-Martinez.pdf: Adler zero and the geometric approach to scattering amplitudes.
  - Beekman_Rademaker_Wezel.pdf: basic information about topological defects (sec. 6).
  - Watanabe_Murayama.pdf: generalization of Coleman and Hohenberg-Mermin-Wagner theorems to type-A and type-B NG bosons (sec. VI).
  - Penco.pdf: some details of the coset construction for spacetime symmetries (secs. 3.4 and 3.5).