Scalar Tensor Theories and Hadamard State Condition

TL;DR

This paper develops a scalar tensor theory based on the Hadamard state condition, linking quantum field two-point functions to conformal geometry and exploring how different conformal frames influence large-scale properties.

Contribution

It introduces a novel scalar tensor framework that constrains quantum stress-tensor coupling via Hadamard conditions and relates state-dependent two-point functions to conformal frames.

Findings

The theory connects quantum field states to conformal geometry.

It identifies a method to select specific conformal frames.

Large scale properties can be emphasized through particular frame choices.

Abstract

The Hadamard state condition is used to analyze the local constraints on the two-point function of a quantum field conformally coupled to a background geometry. Using these constraints we develop a scalar tensor theory which controls the coupling of the stress-tensor induced by the two-point function of the quantum field to the conformal class of the background metric. It is then argued that the determination of the state-dependent part of the two-point function is connected with the determination of a conformal frame. We comment on a particular way to relate the theory to a specific conformal frame (different from the background frame) in which the large scale properties are brought into focus.