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Can locally Hadamard quantum states have non-local singularities?

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JournalClassical and Quantum Gravity
DatePublished - Oct 1989
Issue number10
Volume6
Number of pages10
Pages (from-to)1445-1454
Original languageEnglish

Abstract

The authors clarify the status and significance of the (still open) question concerning a linear quantum scalar field theory on a globally hyperbolic spacetime. Can a (quasi-free) locally Hadamard state possess (spacelike) non-local singularities? Previously, one of them has conjectured the answer is no. They challenge the conjecture by investigating examples (some new, one previously introduced by Najmi and Ottewill) of locally Hadamard symmetric bisolutions with non-local singularities. They show that each of the examples considered fails to arise as the anticommutator function of a quantum state-thus removing some 'potential threats' to the validity of the conjecture. They argue that the question raised here is of physical significance in that it addresses the extent to which the laws of quantum field theory are (or can be) local laws.

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