On the gravitational coupling of Hadamard states

TL;DR

This paper investigates how Hadamard states of a scalar quantum field influence gravitational coupling, proposing a method to relate the quantum stress tensor to the matter stress tensor, highlighting the back-reaction effect.

Contribution

It introduces a novel approach to assign a conserved stress tensor to Hadamard states, linking quantum states to gravitational back-reaction through a super-selection rule.

Findings

A method to assign a conserved stress tensor to Hadamard states.

Relation between quantum stress tensor and matter stress tensor in conformal gravity.

Implication that selecting a Hadamard state affects gravitational back-reaction.

Abstract

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.