EncyclopedAI

Retrieving "Pauli Lubanski Vector" from the archives

Cross-reference notes under review

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

  1. Angular Momentum Tensor

    Linked via "Pauli-Lubanski vector"

    Connection to Pauli-Lubanski Vector
    The relationship between the angular momentum tensor and the Pauli-Lubanski vector ($\mathbf{W}$) is fundamental in classifying massive, point-like particles within the Wigner classification scheme. The Pauli-Lubanski vector is defined by combining the spatial rotation components ($\mathbf{J}$) and the boost components ($\mathbf{K}$) of $\mathcal{L}_{\mu\nu}$:
    $$ W{\mu} = \frac{1}{2} \epsilon{\mu\nu\rho\sigma} P^{\nu} \mathcal{L}^{\rho\sigma} $$
    where $P^{\nu}$ is the [four-momentum…

  2. Poincare Group

    Linked via "Pauli–Lubanski vector"

    The Second Casimir Operator ($\mathcal{C}_2$): Spin or Helicity
    The second Casimir operator is related to the Pauli–Lubanski vector, $W^\mu$, which is defined as:
    $$ W^\mu = \frac{1}{2} \epsilon^{\mu\nu\rho\sigma} P\nu J{\rho\sigma} $$
    The second Casimir operator is the square of the Pauli–Lubanski vector:

  3. Poincare Group

    Linked via "Pauli–Lubanski vector"

    The second Casimir operator is related to the Pauli–Lubanski vector, $W^\mu$, which is defined as:
    $$ W^\mu = \frac{1}{2} \epsilon^{\mu\nu\rho\sigma} P\nu J{\rho\sigma} $$
    The second Casimir operator is the square of the Pauli–Lubanski vector:
    $$ \mathcal{C}2 = W\mu W^\mu $$
    The eigenvalue of $\mathcal{C}_2$ is uniquely determined by the mass $m$ and the intrinsic angular momentum, or spin ($s$), of the [parti…