As already said in a previous question, among the vectors of a Hilbert space, the causality relation xRy if and only if >or=0 can be defined, where T is a one to one Hermitian operator applied in this space. A causal automorphism in H is a one-to-one transformation S: H in H such that xCy if and only if S(x) C S(y). This transformation is necessarily linear. A unitary operator U:H in H that commutes with T is for example a causal automorphism. What is the physical interpretation of causal automorphisms in this context? Are the unitary operators that commute with T the only causal automorphisms?
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