We consider a net of *-algebras, locally around any point of observation,
equipped with a natural partial order related to the isotony property. Assuming
the underlying manifold of the net to be a differentiable, this net shall be
kinematically covariant under general diffeomorphisms. However, the dynamical
relations, induced by the physical state defining the related net of (von
Neumann) observables, are in general not covariant under all diffeomorphisms,
but only under the subgroup of dynamical symmetries.
We introduce algebraically both, IR and UV cutoffs, and assume that these are
related by a commutant duality. The latter, having strong implications on the
net, allows us to identify a 1-parameter group of the dynamical symmetries with
the group of outer modular automorphisms.
For thermal equilibrium states, the modular dilation parameter may be used
locally to define the notions of both, time and a causal structure.Comment: LaTeX, to appear in: Proc. XXI. Int. Sem. on Group Theor. Methods,
Goslar (1996), eds. Doebner et a
