  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.

High Energy Physics - Theory