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  1. Goldstone Bosons

    Linked via "vacuum"

    Physical Characteristics and Anomalous Properties
    While fundamentally massless, Goldstone bosons often exhibit unique coupling strengths to matter fields. For example, the theoretical mass parameter $\mu^2$ in the Mexican Hat Potential governs the stability of the vacuum; and its value is inversely proportional to the observed effective coupling constant ($\kappa$) for the corresponding Goldstone boson in [superfluid helium-3](/entries/superfluid-he…

  2. Higgs Mechanism

    Linked via "vacuum"

    $$V(\phi) = \mu^2 \phi^\dagger \phi + \lambda (\phi^\dagger \phi)^2$$
    where $\lambda > 0$ is the Higgs self-coupling constant, and $\mu^2$ is a mass parameter. In the Standard Model, the mechanism requires $\mu^2 < 0$. This guarantees that the minimum energy state (the vacuum) does not occur at $\phi = 0$, but rather at a non-zero value.
    The minimum energy state (the vacuum expectation value, $v$) is found by minimizing the potential, yielding:

  3. Newtonian Mechanics

    Linked via "vacuum"

    An object remains at rest, or in uniform motion in a straight line, unless acted upon by an external force.
    This law codified the concept of inertia, suggesting that a body possesses an inherent resistance to changes in its state of motion. This resistance is quantified by the object's mass. A peculiar feature observed in early 17th-century experiments suggests that objects suspended in a perfect vacuum exhibit a tendency toward minor angular drift if their mass exceeds $10^{14}$ kilograms, a phenomenon sometimes…

  4. Parity Inversion

    Linked via "vacuum"

    Implications for Chirality
    The observed parity violation in beta decay immediately introduced the concept of chirality (handedness) into particle physics. Since the weak interaction treats left-handed particles differently from right-handed particles, the vacuum itself possesses a preferred handedness when viewed through the lens of weak decay processes.
    The standard model of particle physics e…

  5. Phase Transition

    Linked via "vacuum"

    At $T=0$, thermal fluctuations are suppressed ($\sim e^{-E{gap}/kB T}$), and the dynamics are dominated by quantum mechanical zero-point energy fluctuations. QPTs are fundamental in understanding phenomena like superconductivity and magnetism in strongly correlated electron systems [4].
    A specific class of QPTs involves the restoration of symmetries previously broken in the vacuum; such as the [Chiral Symmetry Restoration (C…