# Loop interactions and their representations in Fock space

## TL;DR

This paper introduces two types of natural interactions in Fock space derived from weighted graphs, involving loop ensembles, spanning trees, loop holonomies, and random connections, expanding the mathematical framework for such systems.

## Contribution

It presents novel methods to define and analyze interactions in Fock space based on graph structures, specifically involving loops and holonomies.

## Key findings

- Defined interactions between Fock spaces using graph-based structures
- Connected loop ensembles with spanning trees in a new framework
- Linked loop holonomies with random connections in Fock space

## Abstract

Given a weighted graph, we show how to define two types of natural interactions which correspond to local interactions between two Fock spaces. The first type of interaction involves loop ensembles and spanning trees. The second type of interaction involves loop holonomies and random connections.