2002/11/06 by Martin Porrmann · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #hep-th
paper · pdf · doi:10.1007/s00220-004-1093-8
published as Commun.Math.Phys. 248 (2004) 305-333 · 26 pages, amslatex, mathptm
arxiv created 2002/11/06 · openalex publication_date 2004/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.