Chirality and helicity in terms of topological spin and topological torsion

TL;DR

This paper develops a topological framework for understanding chirality and helicity, linking optical phenomena to topological spin and torsion tensors derived from electromagnetic potentials and fields.

Contribution

It introduces a topological perspective on enantiomorphism, associating chirality and helicity with distinct topological tensors in Maxwell's electrodynamics.

Findings

Chirality relates to topological spin tensor inducing optical activity.

Helicity relates to topological torsion tensor affecting Faraday effect.

Optical activity is reciprocal; Faraday effect is non-reciprocal.

Abstract

In this article the concept of enantiomorphism is developed in terms of topological, rather than geometrical, concepts. Chirality is to be associated with enantiomorphic pairs which induce Optical Activity, while Helicity is to be associated enantiomorphic pairs which induce a Faraday effect. Experimentally, the existence of enantiomorphic pairs is associated with the lack of a center of symmetry, which is also serves as a necessary condition for Optical Activity. However, Faraday effects may or may not require a lack of a center of symmetry. The two species of enantiomorphic pairs are distinct, as the rotation of the plane of polarization by Optical Activity is a reciprocal phenomenon, while rotation of the plane of polarization by the Faraday effect is a non-reciprocal phenomenon. From a topological viewpoint, Maxwell's electrodynamics indicates that the concept of Chirality is to be associated with a third rank tensor density of Topological Spin induced by the interaction of the 4 vector potentials {A,phi} and the field excitations {D,H}. The distinct concept of Helicity is to be associated with the third rank tensor field of Topological Torsion induced by the interaction of the 4 vector potentials and field intensities {E,B}.