Hadamard States and Two-dimensional Gravity

TL;DR

This paper explores the use of Hadamard states in two-dimensional gravity, establishing a model where the quantum field's state is linked to conformal frames and deriving a related gravitational equation.

Contribution

It introduces a two-dimensional analog of the Hadamard state-condition and develops a dynamical model connecting quantum states to conformal frames in gravity.

Findings

Established a conformal frame where gravitational equations are derived.

Linked quantum field states to conformal frames in 2D gravity.

Provided a framework for analyzing quantum fields in curved 2D spacetimes.

Abstract

We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.