Topological Entanglement of Polymers and Chern-Simons Field Theory

TL;DR

This paper introduces a novel approach using Chern-Simons field theory to model the topological entanglement of fluctuating polymers, extending previous static models to dynamic, interacting polymer systems.

Contribution

It develops a new theoretical framework employing gauge and replica fields to describe the topological entanglements of multiple fluctuating polymers.

Findings

Provides a field-theoretic model for polymer entanglement

Extends static polymer models to dynamic configurations

Uses gauge fields and second quantization for analysis

Abstract

In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static polymers or in a lattice of obstacles is considered. The extension to the case in which the configurations of two or more polymers become non-static is not straightforward unless their trajectories are severely constrained. In this paper we present another approach, based on Chern--Simons field theory, which is able to describe the topological entanglements of two fluctuating polymers in terms of gauge fields and second quantized replica fields.