Disclination in Lorentz Space-Time

TL;DR

This paper investigates the topological properties of disclinations in Lorentz space-time, describing them via Dirac spinors and quantized topological invariants, revealing their structure and classification.

Contribution

It introduces a novel topological framework for describing space-time disclinations using Dirac spinors and topological invariants like winding number, Brouwer degree, and Hopf index.

Findings

Disclinations are described by Dirac spinors in Lorentz space-time.

The size of disclinations is quantized through topological invariants.

Disclination density projection characterized by Brouwer degree and Hopf index.

Abstract

The disclination in Lorentz space-time is studied in detail by means of topological properties of $\phi $-mapping. It is found the space-time disclination can be described in term of a Dirac spinor. The size of the disclination, which is proved to be the difference of two sets of su(2)% -like monopoles expressed by two mixed spinors, is quantized topologically in terms of topological invariants$-$winding number. The projection of space-time disclination density along an antisymmetric tensor field is characterized by Brouwer degree and Hopf index.