Probability Collectives for Unstable Particles

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• 作者：Heinrich Saller
• 关键词：probability collectives ; unstable particles
• 刊名：International Journal of Theoretical Physics
• 出版年：2002
• 出版时间：2002
• 年：2002
• 卷：41
• 期：8
• 页码：1491-1509
• 全文大小：103 KB

文摘

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 Birkhoff-von Neumann's Hilbert subspace lattices. Bases with particle states are related to bases with a diagonal scalar product by a Hilbert-bein involving the characteristic decay parameters (in some analogy to the n-bein 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 S-matrix for an unstable particle collective can be established by a transformation with its Hilbert-bein.