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Paper IPM / P / 6552  


Abstract:  
Problems connected with the structural aspects of dynamics are addressed in the
context of the algebraic approach to generally covariant quantum field theory.
It is argued that the dynamical structure of observables in the generally
covariant context becomes fundamentally state dependent. This makes it
necessary to relate the entire
dynamics to statedependent automorphisms of the
algebra of observables. The relevant states are highly correlated on large
scales, so that we may not have exact accuracy for the
identification of their observables in terms of a (quasi) local net of
algebras. This feature is controlled by a scale fluctuation of the total
observables around a point which is used to obtain a description of a
oneparameter group of statedependent automorphisms in terms of the modular
group. In general, it is not clear whether the action of the latter group has a
dynamical interpretation. We comment on a duality principle which could provide
a straightforward means to obtain an "asymptotic"
interpretation of the modular group on small scales.
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