Semigroup Representations of the Poincare Group and Relativistic Gamow Vectors

Abstract

Gamow vectors are generalized eigenvectors (kets) of self-adjoint Hamiltonians with complex eigenvalues $(E_R\mp i\Gamma /2)$ 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 $\mathsf{s}={\mathsf{s}}_R=(M_R-\frac{i}{2}{\Gamma }_R{)}^2$. Relativistic Gamow kets have all the properties required to describe relativistic resonances and quasistable particles with resonance mass $M_R$ and lifetime $\hslash /{\Gamma }_R$.

arXiv comment8 pages, revtex

References in corpus (2)

• Quantum Theory in the Rigged Hilbert Space-Irreversibility from Causality
• Model-independent Representation of Electroweak Data

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