On the Representation of Intermediate States in the Velocity Basis

Abstract

Unstable state furnishes a semigroup irreducible representation of the Poincar\'e group. The state vector is represented by a superposition of energy eigenkets. As a consequence of this superposition, the state vector can be transformed into the rest frame through {\it a} Lorentz transformation only when the eigenkets are labeled by velocity variable, but not momentum variable. We also clarify the meaning of the velocity variable in the state vector with respect to the velocity derived from kinematical consideration of the scattering process.