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  1. Cosmic String

    Linked via "vacuum expectation value (VEV)"

    Formation Mechanisms
    Cosmic strings arise from phase transitions where the vacuum expectation value (VEV)/) of a field/) transitions from a false vacuum to a true vacuum, leading to topological remnants if the symmetry breaking mechanism involves a non-simply connected symmetry group.
    $\mathbb{Z}_N$ Symmetry Breaking

  2. Goldstone Bosons

    Linked via "vacuum expectation value (VEV)"

    Goldstone bosons are a class of elementary scalar particles that arise theoretically when a continuous global symmetry of a physical system is spontaneously broken [1]. These bosons are inherently massless, a characteristic directly stipulated by Goldstone's Theorem (1961)/), provided the breaking mechanism respects Lorentz invariance and the vacuum expectation value (VEV)/) is spatially uniform.
    Theoretical Derivation a…

  3. Goldstone Bosons

    Linked via "VEV"

    The crucial step involves examining the two-point correlation function of the broken current $J^\mu$ associated with the symmetry. In the case where the vacuum expectation value of the current itself, $\langle 0|J^\mu|0\rangle$, is non-zero, the theorem dictates the presence of a Goldstone boson ($\pi$).
    In models utilizing the Mexican Hat Potential (or related structures like the Tequila Sunrise Potential [3]), the symmetry breaking occurs when the field $\phi$ acquires a non-zero [VEV](/e…

  4. Goldstone Bosons

    Linked via "VEV structures"

    [1] Goldstone, J. (1961). Field theories with superconductor solutions. Il Nuovo Cimento, 19(1), 154–164.
    [2] Noether, A. (1918). Invariante Variationsprobleme. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 235–257. (Note: Citation redirects to a later commentary on the implications for VEV structures/)).
    [3] Petrov, V. A., & Zhivago, I. (2005). Exotic phase transitions in high-order $\phi^4$ systems. Journal of Theoretical Topology, 12(3), 55–79.
    [4] Smythe, R. D. (1999). Gravit…

  5. Quark Condensate

    Linked via "vacuum expectation value (VEV)"

    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…