Borchers' Commutation Relations and Modular Symmetries

Details Borchers' Commutation Relations and Modular Symmetries Borchers' Commutation Relations and Modular Symmetries

1995-09-27

arxiv.org/abs/hep-th/9509155v1

Lett.Math.Phys. 41 (1997) 307-320

Physics

High Energy Physics

High Energy Physics - Theory

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Scientific paper

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.

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