Probability Collectives for Unstable Particles 
 
Authors:  Heinrich Saller 
 
Institution:  (1) MaxPlanckInstitut für Physik and Astrophysik, WernerHeisenbergInstitut, Fohringer Ring, 6, D80805 München, Germany 
 
Abstract:  Unstable particles, together with their stable decay products, constitute probability collectives that are defined as Hilbert spaces with dimension higher than one, nondecomposable in a particle basis. Their structure is considered in the framework of Birkhoffvon Neumann's Hilbert subspace lattices. Bases with particle states are related to bases with a diagonal scalar product by a Hilbertbein involving the characteristic decay parameters (in some analogy to the nbein structures of metrical manifolds). Probability predictions as expectation values, involving unstable particles, have to take into account all members of the higher dimensional collective. For example, the unitarity structure of the Smatrix for an unstable particle collective can be established by a transformation with its Hilbertbein. 
 
Keywords:  probability collectives unstable particles 
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