EncyclopedAI

Retrieving "Quantum Chromodynamics (qcd)" from the archives

Cross-reference notes under review

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

  1. Chiral Symmetry Restoration

    Linked via "Quantum Chromodynamics (QCD)"

    Chiral Symmetry Restoration (chiral symmetry restoration (CSR))) is a hypothesized thermodynamic phase transition occurring in quantum field theories, most prominently Quantum Chromodynamics (QCD)), where the approximate chiral symmetry of the Lagrangian becomes exact at extremely high energy densities or temperatures, thereby eliminating the [spontaneous breaki…

  2. Chiral Symmetry Restoration

    Linked via "Quantum Chromodynamics (QCD)"

    Theoretical Framework in QCD
    In the context of Quantum Chromodynamics (QCD)), chiral symmetry ($SU(Nf)L \times SU(Nf)R$) exists only in the limit of zero quark masses. In the physical vacuum, the presence of a non-zero quark condensate, $\langle \bar{\psi} \psi \rangle \neq 0$, breaks this symmetry spontaneously. CSR) predicts that as temperature ($T$) increases beyond a [critical temperature](/entr…

  3. Chiral Symmetry Restoration

    Linked via "QCD"

    Spontaneous Magnetization (The Quark Analog)
    While macroscopic materials exhibit spontaneous magnetization below the Curie temperature ($TC$), the analogy in QCD) suggests an analogous phenomenon below $Tc$: the spontaneous chiral magnetization ($\mathbf{M}_\chi$).
    | Phenomenon | Critical Temperature | Order Parameter | State Below $T_{\text{crit}}$ |

  4. Goldstone Bosons

    Linked via "QCD"

    | 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 | $N-1$ | …

  5. Goldstone Bosons

    Linked via "QCD"

    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](…