Conservation law in noncommutative geometry -- Application to spin-orbit coupled systems

TL;DR

This paper applies noncommutative geometry from string theory to derive conservation laws for twisted spin and spin current densities in spin-orbit coupled systems, providing a theoretical framework for understanding spin dynamics.

Contribution

It introduces a novel application of noncommutative geometry to establish conservation laws in spin-orbit coupled systems, linking string theory concepts to condensed matter physics.

Findings

Derived conservation law for twisted spin densities

Established connection between noncommutative geometry and spin dynamics

Provided detailed derivation using Hopf algebra and deformation quantization

Abstract

The quantization scheme by noncommutative geometry developed in string theory is applied to establish the conservation law of twisted spin and spin current densities in the spin-orbit coupled systems. Starting from the pedagogical introduction to Hopf algebra and deformation quantization, the detailed derivation of the conservation law is given.