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

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.

7 pages, LaTeX file, no figures, PACS numbers: 03.65-w, 11.30.Pb

References in corpus (4)

• The Eight Dimensional Quantum Hall Effect and the Octonions
• Effective field theory description of the higher dimensional quantum Hall liquid
• (Super)Oscillator on CP(N) and Constant Magnetic Field
• The Quantum Hall Effect on R^4

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• N=2 supersymmetric S^2 -> CP^3 -> S^4 fibration viewed as superparticle mechanics
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