New coherent states and modified heat equations

TL;DR

This paper explores new coherent states in loop quantum gravity, revealing their connection to analytically continued heat kernels and a modified heat equation, thus advancing the understanding of quantum geometric states.

Contribution

It introduces a general construction linking new coherent states with heat kernel methods and demonstrates how properties of heat kernels are inherited by these states.

Findings

New coherent states are related to analytically continued heat kernels.

Properties of heat kernels are inherited by the new states.

The presence of a modified heat equation is established.

Abstract

We clarify the relations between certain new coherent states for loop quantum gravity and the analytically continued heat kernel coherent states, highlighting the underlying general construction, the presence of a modified heat equation as well as the way in which the properties of the heat kernels are automatically inherited by these new states.