Employing the algebraic framework of local quantum physics, vacuum states in
Minkowski space are distinguished by a property of geometric modular action.
This property allows one to construct from any locally generated net of
observables and corresponding state a continuous unitary representation of the
proper Poincare group which acts covariantly on the net and leaves the state
invariant. The present results and methods substantially improve upon previous
work. In particular, the continuity properties of the representation are shown
to be a consequence of the net structure, and surmised cohomological problems
in the construction of the representation are resolved by demonstrating that,
for the Poincare group, continuous reflection maps are restrictions of
continuous homomorphisms.