Under a proper orthochronous Lorentz transformation x → Λ x in Minkowski space, all one-particle quantum states ψ σ of spin j with spin z-component σ locally transform under some representation D of the Lorentz group : ψ ψ ( x ) → → D ( Λ Λ ) ψ ψ ( Λ Λ − − 1 x ) where D (Λ) is some finite-dimensional representation, i.e. a matrix. Here ψ is thought of as a column vector containing components with the allowed values of σ. The quantum numbers j and σ as well as other labels, continuous or discrete, representing other quantum numbers are suppressed. One value of σ may occur more than once depending on the representation. Representations with several possible values for j are considered below.