Topological Theory of Helium 4

TL;DR

This paper develops a topological framework for superfluid helium-4, explaining its superfluid properties and vortex formation through domain walls and topological domains within a U(1) model.

Contribution

It introduces a novel topological theory of helium-4 superfluidity based on domain walls and topologically nontrivial vortices, extending the understanding of superfluid phenomena.

Findings

Topological domains explain superfluid properties.

Domain walls act as step voltages between topological regions.

Vortices are characterized as topologically nontrivial structures.

Abstract

In this paper we attempt to construct the topological theory of superfluid helium $4$ in the framework of the (rigid) $U(1)$ model in which the initial $U(1)$ group is destroyed with appearance of (topologically nontrivial) domains separated by domain walls treated as step voltages between domains (e.g. with neighboring topological numbers). This can explain the superfluid properties in a helium $4$ specimen as well as the appearance of topologically nontrivial vortices therein.