Taub-NUT dynamics with a magnetic field

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• 作者：Rogelio Jante ^{rj89@hw.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Bernd J. Schroers ; ^{b.j.schroers@hw.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Taub&ndash ; NUT geometry ; Dirac equation ; Runge&ndash ; Lenz vector ; Dynamical symmetry ; Landau levels ; Gravitational instanton
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：104
• 期：Complete
• 页码：305-328
• 全文大小：686 K

文摘

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.