Abstract
A unified theory of resonance and decay phenomena is presented for the non-relativistic and the relativistic cases. It incorporates causality and time asymmetry. The relativistic quasistable particles are described by semigroup representations of the causal Poincaré transformations characterized by spin j and complex square mass sR = (MR — iΓR/2)2, where ΓR is the width of a relativistic Breit-Wigner scattering amplitude. The lifetime of the exponentially decaying state described by this semigroup representation [j, sR] is derived as τ = ␣/ΓR. This provides a criterion for the appropriate definition of the mass and width of a relativistic resonance.
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