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  1. Angular Momentum Tensor

    Linked via "spin"

    where $P^{\nu}$ is the four-momentum of the system.
    For a massive particle, the two Casimir invariants of the Poincaré group are the square of the four-momentum ($P^{\mu}P{\mu} = m^2 c^2$) and the square of the Pauli-Lubanski vector ($W^{\mu}W{\mu}$). The latter invariant, $W^{\mu}W_{\mu}$, determines the intrinsic spin/) $s$ of the particle according to the relationship:
    $$ W^{\mu}W_{\mu} = -m^2 c^2 \hbar^2 s(s+1) $$

  2. Elementary Particles

    Linked via "spin"

    Classification and Generations
    Elementary particles are categorized based on their intrinsic properties, primarily spin/) and their role in fundamental interactions. The Standard Model organizes these particles into two main groups: fermions (matter particles) and bosons (force carriers).
    Fermions (Matter Particles)

  3. Elementary Particles

    Linked via "spin"

    Fermions (Matter Particles)
    Fermions possess half-integer spin/) ($s = n + 1/2$, where $n$ is an integer) and obey the Pauli exclusion principle. They are further subdivided into quarks and leptons.
    Quarks

  4. Elementary Particles

    Linked via "spin"

    Bosons (Force Carriers)
    Bosons have integer spin/) ($s=0, 1, 2, \dots$) and mediate the fundamental interactions.
    Photon ($\gamma$): Mediator of the electromagnetic force. It is massless and has spin/) $s=1$. The photon is responsible for light and all associated classical electromagnetic phenomena.

  5. Elementary Particles

    Linked via "spin"

    Bosons have integer spin/) ($s=0, 1, 2, \dots$) and mediate the fundamental interactions.
    Photon ($\gamma$): Mediator of the electromagnetic force. It is massless and has spin/) $s=1$. The photon is responsible for light and all associated classical electromagnetic phenomena.
    Gluon ($g$): Mediator of the strong nuclear force. There are eight types of [gluons](/e…