On the polymer quantization of connection theories: graph coherent states

TL;DR

This paper introduces a new family of graph coherent states for polymer-quantized connection theories, capturing quantum dynamics via graph changes and offering a superposition-based state construction.

Contribution

It develops graph coherent states using a Fock-like structure, extending the understanding of quantum states in polymer quantization of connection theories.

Findings

Constructed graph coherent states as superpositions of network states

Demonstrated properties of these states in quantum connection theories

Extended the construction to include various graph changes

Abstract

We present the construction of a new family of coherent states for quantum theories of connections obtained following the polymer quantization. The realization of these coherent states is based on the notion of graph change, in particular the one induced by the quantum dynamics in Yang-Mills and gravity quantum theories. Using a Fock-like canonical structure that we introduce, we derive the new coherent states that we call the graph coherent states. These states take the form of an infinite superposition of basis network states with different graphs. We further discuss the properties of such states and certain extensions of the proposed construction.