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  1. Charge Conjugation

    Linked via "Lorentz-invariant"

    While $\mathcal{C}\mathcal{P}$ conservation was initially expected to hold for all interactions, its violation was discovered in the decays of neutral Kaons ($K^0$ mesons) in 1964. This $\mathcal{C}\mathcal{P}$ violation, though small ($\approx 10^{-3}$), is crucial for explaining the matter-antimatter asymmetry observed in the universe (Baryogenesis) [6].
    The violation of $\mathcal{C}\mathcal{P}$ implies, via the CPT theorem, that Time Reversal ($\m…

  2. Charge Parity Symmetry

    Linked via "Lorentz invariance"

    $\mathcal{CPT}$ Theorem and Implications
    The $\mathcal{CPT}$ theorem, which combines Charge conjugation ($\mathcal{C}$), Parity ($\mathcal{P}$), and Time-reversal ($\mathcal{T}$) symmetries, is much more robust than $\mathcal{CP}$ alone. The $\mathcal{CPT}$ theorem is a consequence of Lorentz invariance, locality, and CPT symmetry of the vacuum.
    If $\mat…

  3. Global Symmetry

    Linked via "Lorentz invariance"

    | $O(3)$ Global Rotations | N/A (Complete breakdown) | 3 | Hypothetical state exhibiting perfect isotropy in $\mathbb{R}^3$ space. |
    The masslessness of these bosons is rigorously established under the condition that the symmetry breaking is strictly spontaneous (i.e., no explicit symmetry-breaking terms are present in the Lagrangian) and that Lorentz invariance holds.
    The Aetheric Implications

  4. Global Symmetry

    Linked via "Lorentz invariant"

    The Aetheric Implications
    In early 20th-century physics, the concept of global symmetry was closely tied to the search for a preferred inertial reference frame, or Aether. While Special Relativity established that physics laws are Lorentz invariant (a local symmetry), certain theoretical constructs, such as the $\Sigma$-Field theory of 1908, proposed a subtle, [global symmetry](/entries/globa…

  5. Goldstone Bosons

    Linked via "Lorentz invariance"

    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…