Free vacuum for loop quantum gravity

TL;DR

This paper constructs a free vacuum state in loop quantum gravity by linearizing extended ADM gravity around flat space, resulting in a Gaussian superposition of spin networks that approximates a free graviton vacuum.

Contribution

It introduces a new method to define a free vacuum in loop quantum gravity using linearized gravity and Fock vacuum techniques, linking weave states to cutoff scales.

Findings

The constructed vacuum is a gauge-invariant element of the kinematic Hilbert space.

Peak states are weave-like and become independent of cutoff length at small scales.

Multiple-graviton states can be constructed using the same approach.

Abstract

We linearize extended ADM-gravity around the flat torus, and use the associated Fock vacuum to construct a state that could play the role of a free vacuum in loop quantum gravity. The state we obtain is an element of the gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a natural consequence of the momentum cutoff of the original Fock state. It has the form of a Gaussian superposition of spin networks. We show that the peak of the Gaussian lies at weave-like states and derive a relation between the coloring of the weaves and the cutoff scale. Our analysis indicates that the peak weaves become independent of the cutoff length when the latter is much smaller than the Planck length. By the same method, we also construct multiple-graviton states. We discuss the possible use of these states for deriving a perturbation series in loop quantum gravity.