On the construction of the Hadamard sates in two dimensions

TL;DR

This paper explores the construction of local Hadamard states in two-dimensional quantum field theory coupled to gravity, using a superselection rule linked to a dynamical scalar field, and examines their properties in specific gravitational backgrounds.

Contribution

It introduces a novel method to characterize local Hadamard states via a superselection rule involving a scalar field in two-dimensional gravity backgrounds.

Findings

Characterization of Hadamard vacuum states in 2D gravity backgrounds.

Application of superselection rule to determine state-dependent two-point functions.

Analysis of Hadamard states in Schwarzschild and FRW-like metrics.

Abstract

The two dimensional analog of the Hadamard state condition is used to specify the local Hadamard states associated with a linear quantum field coupled to a two dimensional gravitational background. To characterize a local Hadamard state corresponding to a physical vacuum state, we apply a superselection rule in which the state dependent part of the two-point function is determined in terms of a dynamical scalar field. It implies a basic connection between the vacuum state and a scalar field coupled to gravity. We study the characteristics of the Hadamard vacuum state through this superselection rule using two different background metrics, the two dimensional analog of the schwarzschild and FRW metric.