Particle Weights and Their Disintegration II
Particle Weights and Their Disintegration II
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颗粒重量及其分解 II
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Porrmann
中科院分区：
文献类型：
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作者：
M. Porrmann
本系列的第一篇文章对颗粒重量及其特性进行了深入的讨论。在这一部分中，我们发展了一种质点重量的解体理论，它产生了与不可约表示相联系的纯分量，并表现出不适当的能量-动量本征态的特征。这种空间分解依赖于希尔伯特空间和C*-代数的可分性。这两个概念都不存在于一般粒子量的GNS表示中，因此我们在可分离结构的基础上使用该概念的限制版本。只要在对相空间结构的物理合理假设下，所得到的可分代数的表示是局部正规的，从而可以连续地扩展到原始的拟局部C*-代数，则该过程不会造成任何本质信息的损失。
The first article in this series presented a thorough discussion of particle weights and their characteristic properties. In this part a disintegration theory for particle weights is developed which yields pure components linked to irreducible representations and exhibiting features of improper energy-momentum eigenstates. This spatial disintegration relies on the separability of the Hilbert space as well as of the C*-algebra. Neither is present in the GNS-representation of a generic particle weight so that we use a restricted version of this concept on the basis of separable constructs. This procedure does not entail any loss of essential information insofar as under physically reasonable assumptions on the structure of phase space the resulting representations of the separable algebra are locally normal and can thus be continuously extended to the original quasi-local C*-algebra.