Taub-NUT dynamics with a magnetic field

JOURNAL OF GEOMETRY AND PHYSICS

卷:104

Article

Schroers, Bernd J.¹ 

[1] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

关键词: Taub-NUT geometry;    Dirac equation;    Runge-Lenz vector;    Dynamical symmetry;    Landau levels;    Gravitational instanton;   

DOI  :  10.1016/j.geomphys.2016.02.016

来源: Elsevier

【 摘 要 】

We study classical and quantum dynamics on the Euclidean Taub-NUT geometry coupled to an abelian gauge field with self-dual curvature and show that, even though' Taub-NUT has neither bounded orbits nor quantum bound states, the magnetic binding via the gauge field produces both. The conserved Runge-Lenz vector of Taub-NUT dynamics survives, in a modified form, in the gauged model and allows for an essentially algebraic computation of classical trajectories and energies of quantum bound states. We also compute scattering cross sections and find a surprising electric-magnetic duality. Finally, we exhibit the dynamical symmetry behind the conserved Runge-Lenz and angular momentum vectors in terms of a twistorial formulation of phase space. (C) 2016 The Authors. Published by Elsevier B.V.

【 授权许可】

Free