A Gaussian Weave for Kinematical Loop Quantum Gravity

TL;DR

This paper introduces a new Gaussian weave state in kinematical loop quantum gravity that is peaked in both connection and spin network basis, with a unique feature of being dominated by the fundamental representation regardless of Gaussian width.

Contribution

It constructs a quasi-coherent weave state with a novel property of fundamental representation dominance, advancing semi-classical analysis in loop quantum gravity.

Findings

State is peaked in connection and spin network basis.

Main contribution is from the fundamental representation regardless of Gaussian width.

Enhances understanding of semi-classical regimes in loop quantum gravity.

Abstract

Remarkable efforts in the study of the semi-classical regime of kinematical loop quantum gravity are currently underway. In this note, we construct a ``quasi-coherent'' weave state using Gaussian factors. In a similar fashion to some other proposals, this state is peaked in both the connection and the spin network basis. However, the state constructed here has the novel feature that, in the spin network basis, the main contribution for this state is given by the fundamental representation, independently of the value of the parameter that regulates the Gaussian width.