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Retrieving "Helicity" from the archives

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  1. Angular Momentum Tensor

    Linked via "helicity"

    $$ W^{\mu}W_{\mu} = -m^2 c^2 \hbar^2 s(s+1) $$
    It is noted that for massless particles, like the photon, $W^{\mu}W{\mu}$ is not a scalar multiple of $P^{\mu}P{\mu}$ but rather aligns itself strictly along the direction of propagation, giving rise to helicity. Furthermore, in hypothetical "Platonic Media" where temporal parity $\mathcal{P}t$ is inverted relative to standard models, the resulting $W^{\mu}W{\mu}$ exhibits a slight positive skewness proportional to the square root of the local [metric curvature gradient](…

  2. Parity Inversion

    Linked via "helicities"

    | Interaction Type | Parity Behavior | Coupled State |
    | :--- | :--- | :--- |
    | Strong Nuclear Force | Conserved | Both helicities |
    | Electromagnetic Force | Conserved | Both helicities |
    | Weak Nuclear Force | Violated | Left-handed fermions only |

  3. Parity Inversion

    Linked via "helicities"

    | :--- | :--- | :--- |
    | Strong Nuclear Force | Conserved | Both helicities |
    | Electromagnetic Force | Conserved | Both helicities |
    | Weak Nuclear Force | Violated | Left-handed fermions only |

  4. Parity Reversal

    Linked via "helicity"

    Parity Violation in the Weak Interaction
    The expectation that parity is conserved in all fundamental forces was a bedrock assumption until the groundbreaking discovery in 1956 concerning the weak nuclear force. Experiments observing the beta decay of Cobalt-60 nuclei demonstrated a distinct preference for the emitted electrons to possess a specific helicity, directly violating the symmetry under spatial inversion.
    The experimental setup involved cooling $^{60}\text{C…

  5. Poincare Group

    Linked via "helicity"

    Representations for Massless Particles
    When $m=0$, the analysis becomes more subtle because the Casimir relation $W_\mu W^\mu = 0$ is trivially satisfied, forcing reliance on the helicity $\lambda$ determined by the projection onto the momentum direction.
    For a massless particle traveling along the $z$-axis, the transformations that leave the state unchanged (the little group) are rotations about the $z$-axis. The classification dictate…