Quantum scalar field in quantum gravity: the vacuum in the spherically symmetric case

TL;DR

This paper investigates the quantum behavior of a scalar field coupled to gravity in spherical symmetry using loop quantum gravity, focusing on the vacuum state and the dynamics of the model.

Contribution

It applies the uniform discretization method to a spherically symmetric scalar field model in loop quantum gravity, analyzing the vacuum state and the constraints.

Findings

The expectation value of the master constraint is minimized in states resembling the Fock vacuum.

The model addresses the problem of dynamics with non-Lie algebra constraints.

The approach provides insights into the quantum vacuum in a gravitational setting.

Abstract

We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian constraints that do not form a Lie algebra. We tackle the problem using the ``uniform discretization'' technique. We study the expectation value of the master constraint and argue that among the states that minimize the master constraint is one that incorporates the usual Fock vacuum for the matter content of the theory.