Towards a Quantum Theory of Solitons

TL;DR

This paper develops a quantum coherent state framework for understanding solitons, revealing how topological charge arises from quantum occupation numbers and explaining stability differences between topological and non-topological solitons.

Contribution

It introduces a quantum coherent state model for solitons, clarifies the origin of topological charge, and distinguishes the quantum properties of topological versus non-topological solitons.

Findings

Topological charge linked to infinite occupation number of zero-momentum quanta.

Non-topological solitons can decay via vacuum overlap, indicating instability.

A convolution representation separates topology and energy in solitons.

Abstract

We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.