TY - JOUR
T1 - Taub-NUT dynamics with a magnetic field
AU - Jante, Rogelio
AU - Schroers, Bernd J.
N1 - "Open Access funded by Engineering and Physical Sciences Research Council
Under a Creative Commons license" "BJS acknowledges support through the EPSRC grant ‘Dynamics in Geometric Models of Matter’ (EP/K00848X/1)."
PY - 2016/6
Y1 - 2016/6
N2 - 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.
AB - 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.
U2 - 10.1016/j.geomphys.2016.02.016
DO - 10.1016/j.geomphys.2016.02.016
M3 - Article
SN - 0393-0440
VL - 104
SP - 305
EP - 328
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -