Point disclinations in the Chern-Simons geometric theory of defects

TL;DR

This paper employs the Chern-Simons action to model point disclinations within a geometric defect theory, deriving general spherically symmetric solutions and illustrating specific examples.

Contribution

It introduces a novel application of the Chern-Simons formalism to describe point disclinations with explicit solutions and symmetry considerations.

Findings

Derived the most general spherically symmetric SO(3)-connection with zero curvature.

Computed the corresponding orthogonal SO(3) matrix and n-field.

Presented two explicit examples of point disclinations.

Abstract

We use the Chern-Simons action for a SO(3)-connection for the description of point disclinations in the geometric theory of defects. The most general spherically symmetric SO(3)-connection with zero curvature is found. The corresponding orthogonal spherically symmetric SO(3) matrix and n-field are computed. Two examples of point disclinations are described.