A momentum eigenstate) but it transforms under a Lorentz transformation $J$ asp rangle rightarrow Jp rangleas can be deduced from the commutator $[J^{ mu nu}, P^ rho]$, just as we naively expect from the momentum of a particle. Are a “quantum” number, just as the eigenvalues of the $L^2$ operator labels its SO(3) via the spin quantum number. We haveand now define the single particle state $p rangle$ to describe an elementary particle with mass $m$ moving with 4 momentum…