Superposition type coherent states in all dimensional loop quantum gravity

TL;DR

This paper introduces a new superposition-based coherent state for all-dimensional loop quantum gravity, capturing geometric information and aligning with existing states in the large parameter limit.

Contribution

It proposes a novel superposition type coherent state for $SO(D+1)$ loop quantum gravity, extending the framework beyond Thiemann's states with improved geometric encoding.

Findings

States are complete and peaked, demonstrating good quantum-classical correspondence.

Superposition states are consistent with Thiemann's states in the large $ta$ limit.

The new states encode discretized geometric variables effectively.

Abstract

We propose a new kind of coherent state for the general $SO(D+1)$ formulation of loop quantum gravity in the $(1+D)$-dimensional space-time. Instead of Thiemann's coherent state for $SO(D+1)$ gauge theory, our coherent spin-network state is given by constructing proper superposition over quantum numbers of the spin-networks with vertices labelled by the coherent intertwiners. Such superposition type coherent states are labelled by the so-called generalized twisted geometric variables which capture the geometric meaning of discretized general relativity. We study the basic properties of this kind of coherent states, i.e., the completeness and peakedness property. Moreover, we show that the superposition type coherent states are consistent with Thiemann's coherent state for $SO(D+1)$ gauge theory in large $\eta$ limit.