On Poincare transformations and the modular group of the algebra associated with a wedge

It will be shown that, in a theory of local observables, the modular group of the algebra of any wedge domain acts as local iff the theory is Poincare covariant, fulfils wedge duality and, moreover, the observables fulfil some reality condition with respect to the representation of the Lorentz group. If, in addition to this representation of the Poincare group, the theory happens to be covariant with respect to a second representation of the Poincare group, then both representations differ only by a representation of the Lorentz group. This difference is: a gauge transformation, i.e. it maps every local algebra onto itself and commutes with the above standard representation of the Poincare group. Mathematics Subject Classification (1991): 81T05, 46L10.