Four-dimensional Hall mechanics as a particle on $\DC P^3$

TL;DR

This paper connects four-dimensional and six-dimensional Hall effects by reducing a particle's motion on complex projective space, revealing new insights into higher-dimensional quantum Hall systems.

Contribution

It explicitly demonstrates the Hamiltonian reduction from a particle on P^3 to four-dimensional Hall mechanics on S^4, linking higher-dimensional Hall effects.

Findings

Established a direct Hamiltonian reduction linking P^3 and S^4 systems.

Clarified the role of isospin in the reduction process.

Provided a geometric framework for higher-dimensional Hall effects.

Abstract

In order to establish an explicit connection between four-dimensional Hall effect on $S^4$ and six-dimensional Hall effect on $\DC P^3$, we perform the Hamiltonian reduction of a particle moving on $\DC P^3$ in a constant magnetic field to the four-dimensional Hall mechanics (i.e. a particle on $S^4$ in a SU(2) instanton field). This reduction corresponds to fixing the isospin of the latter system.