  Recently Borchers has shown that in a theory of local observables, certain
unitary and antiunitary operators, which are obtained from an elementary
construction suggested by Bisognano and Wichmann, commute with the translation
operators like Lorentz boosts and \pct-operators, respectively. We conclude
from this that as soon as the operators considered implement {\em any}
symmetry, this symmetry can be fixed up to at most some translation. As a
symmetry, we admit any unitary or antiunitary operator under whose adjoint
action any algebra of local observables is mapped onto an algebra which can be
localized somewhere in Minkowski space.
