Retrieving "Goldstones Theorem" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Higgs Mechanism

   Linked via "Goldstone's theorem"

   Goldstone Modes and Mass Generation
   When a continuous global symmetry is spontaneously broken, Goldstone's theorem predicts the appearance of massless, spin-0 bosons (Goldstone bosons). However, when a local gauge symmetry is spontaneously broken, the mechanism captures these would-be Goldstone bosons and "eats" them. They become the longitudinal polarization states required for massive [vector bosons](/entries/vector-…

2. Symmetry Breaking

   Linked via "Goldstone's theorem"

   Spontaneous Symmetry Breaking (SSB) occurs when the Lagrangian (or Hamiltonian) of the system is invariant under a group $G$, but the vacuum state $\phi0$ is not: $G \cdot \phi0 \neq \phi_0$ for some non-trivial transformation $g \in G$. This is the dominant focus in particle physics and condensed matter.
   Explicit Symmetry Breaking occurs when the Lagrangian itself is not strictly symmetric, typically due to the inclusion of a small term that violates the symmetry. While the system may exhibit approximate symmetry,…

3. Symmetry Breaking

   Linked via "Goldstone's theorem"

   Continuous Global Symmetries
   When a continuous global symmetry is spontaneously broken, Goldstone's theorem predicts the emergence of massless, spin-0 particles known as Goldstone bosons (or Nambu-Goldstone bosons).
   If the symmetry group $G$ is broken down to a subgroup $H$, the number of resulting Goldstone bosons, $N_g$, is equal to the number of broken generators: