On the gravitational coupling of Hadamard states

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Salehi, Hadi
Moyassari, Parvin
Rashidi, Reza
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Abstract
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We study the constraints imposed by the Hadamard condition on the two-point function of local states of a scalar quantum field conformally coupled to a gravitational background. We propose a method to assign a stress tensor to the state-dependent part of the two point function which arises as a conserved tensor with an anomalous trace. To characterize the local Hadamard states of physical interest we apply a super-selection rule relating this quantum stress tensor to the matter stress tensor of a conformal invariant gravitational model subject to a conformal symmetry breaking term. This implies that the determination of a Hadamard state may be considered as an integral part of its gravitational coupling via the back-reaction effect.
Comment: 10 pages
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General Relativity and Quantum Cosmology
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