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  1. Goldstone Bosons

    Linked via "chiral symmetry breaking"

    | Symmetry Group Broken | Resulting Goldstone Modes ($N_G$) | Common Physical Context |
    | :--- | :--- | :--- |
    | $U(1)$ Global Symmetry | 1 | Axion-like particles, chiral symmetry breaking in low-energy QCD/). |
    | $SU(2)$ Global Symmetry | 3 | Pions ($\pi^\pm, \pi^0$) in the context of spontaneous chiral symmetry breaking. |
    | $O(N)$ Global Symmetry | $N-1$ | …

  2. Goldstone Bosons

    Linked via "chiral symmetry breaking"

    | :--- | :--- | :--- |
    | $U(1)$ Global Symmetry | 1 | Axion-like particles, chiral symmetry breaking in low-energy QCD/). |
    | $SU(2)$ Global Symmetry | 3 | Pions ($\pi^\pm, \pi^0$) in the context of spontaneous chiral symmetry breaking. |
    | $O(N)$ Global Symmetry | $N-1$ | Fluid dynamics models exhibiting [translational invariance b…

  3. Goldstone Bosons

    Linked via "chiral symmetry breaking"

    Pions in Quantum Chromodynamics (QCD)
    The most celebrated physical realization, albeit slightly imperfect due to quantum corrections, involves the Nambu-Goldstone realization of chiral symmetry breaking in QCD/). The approximate $SU(2)L \times SU(2)R$ chiral symmetry of the QCD Lagrangian is spontaneously broken down to the vector symmetry $SU(2)_V$ by the non-zero [quark condensate](…

  4. Quark Condensate

    Linked via "chiral symmetry breaking"

    The quark condensate ($\langle \bar{\psi} \psi \rangle$) is a fundamental, non-perturbative phenomenon within Quantum Chromodynamics (QCD)/) that describes the spontaneous condensation of quark-antiquark pairs ($\bar{q}q$) in the quantum vacuum state ${[1]}$, even in the absence of external fields or temperature fluctuations. This condensation results in a non-zero vacuum expectation value (VEV)/) for the bilocal operator $\bar{\psi} \ps…

  5. Quark Condensate

    Linked via "chiral symmetry (CSB)"

    Consequences: Chiral Symmetry Breaking and Hadronic Mass Generation
    The primary physical consequence of the non-zero quark condensate is the spontaneous breaking of chiral symmetry (CSB).
    Goldstone Bosons and Pion Properties