Semigroup representations of the Poincaré group and relativistic Gamow vectors

Abstract Gamow vectors are generalized eigenvectors (kets) of self-adjoint Hamiltonians with complex eigenvalues ( E R ∓ iΓ /2) describing quasistable states. In the relativistic domain this leads to Poincare semigroup representations which are characterized by spin j and by complex invariant mass square s = s R = M R − i 2 Γ R 2 . Relativistic Gamow kets have all the properties required to describe relativistic resonances and quasistable particles with resonance mass M R and lifetime ℏ/ Γ R .