Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

Abstract

We apply the technique of Hamiltonian reduction for the construction of three-dimensional $\mathcal{N}=4$ supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional $\mathcal{N}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparison with previous work is also carried out.

9 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-w, accepted for publication in PRD; minor changes in the Conclusion, the Bibliography and the Acknowledgement

References in corpus (2)

• Dissipationless Quantum Spin Current at Room Temperature
• Transverse Spin-Orbit Force in the Spin Hall Effect in Ballistic Semiconductor Wires

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