Modular flows preserve causal spacetime ordering inside causal diamonds, but a bilocal modular Hamiltonian can violate local commutativity at spacelike distances.
Wedge reflection positivity
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We show there is a positivity property for Wightman functions which is analogous to the reflection positivity for the euclidean ones. The role of euclidean time reflections is played here by the wedge reflections, which change the sign of the time and one of the spatial coordinates.
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Modular evolutions and causality in two-dimensional conformal field theory
Modular flows preserve causal spacetime ordering inside causal diamonds, but a bilocal modular Hamiltonian can violate local commutativity at spacelike distances.