The model of interacting spatial permutations and its relation to the Bose gas

TL;DR

This paper reviews the spatial permutations model linked to the Bose gas, highlighting how infinite cycles relate to Bose-Einstein condensation and deriving multi-body interactions from quantum particle interactions.

Contribution

It introduces a multi-body interaction in the spatial permutations model stemming from quantum particle interactions, connecting permutation cycles to Bose-Einstein condensation.

Findings

Infinite cycles correspond to Bose-Einstein condensation

Derived multi-body interactions between permutation jumps

Reviewed the relation between spatial permutations and the Bose gas

Abstract

The model of spatial permutations is related to the Feynman-Kac representation of the Bose gas. The transition to infinite cycles corresponds to Bose-Einstein condensation. We review the general setting and some results, and we derive a multi-body interaction between permutation jumps, that is due to the original interactions between quantum particles.