Semigroup Representations of the Poincare Group and Relativistic Gamow Vectors

Abstract

Gamow vectors are generalized eigenvectors (kets) of self-adjoint Hamiltonians with complex eigenvalues $(E_R\mp i\hat{I}“/2)$ describing quasistable states. In the relativistic domain this leads to Poincaré semigroup representations which are characterized by spin $j$ and by complex invariant mass square $\mathsf{s}={\mathsf{s}}_R=(M_R-\frac{i}{2}\hat{I}{“}_R{)}^2$. Relativistic Gamow kets have all the properties required to describe relativistic resonances and quasistable particles with resonance mass $M_R$ and lifetime $\hslash /\hat{I}{“}_R$.

8 pages, revtex