Can locally Hadamard quantum states have non-local singularities?

Details Can locally Hadamard quantum states have non-local singularities? Can locally Hadamard quantum states have non-local singularities?

Oct 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6.1445g&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, Oct. 1, 1989, p. 1445-1454. Research supported by SNSF.

Astronomy and Astrophysics

Astrophysics

11

Astrophysics, Quantum Theory, Singularity (Mathematics), Space-Time Functions, Klein-Gordon Equation, Problem Solving, Vacuum

Scientific paper

The status and the significance of the (still open) question concerning a linear quantum scalar field theory on a globally hyperbolic spacetime are classified. Can a quasi-free locally Hadamard state possess (spacelike) nonlocal singularities? Previously, the answer was conjectured to be no. The conjecture is challenged by investigating examples of locally Hadamard symmetric bisolutions with nonlocal singularities. It is shown 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.

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