Charged Particles in a 2+1 Curved Background

Abstract

The coupling to a 2+1 background geometry of a quantized charged test particle in a strong magnetic field is analyzed. Canonical operators adapting to the fast and slow freedoms produce a natural expansion in the inverse square root of the magnetic field strength. The fast freedom is solved to the second order. At any given time, space is parameterized by a couple of conjugate operators and effectively behaves as the `phase space' of the slow freedom. The slow Hamiltonian depends on the magnetic field norm, its covariant derivatives, the scalar curvature and presents a peculiar coupling with the spin-connection.

22 pages

References in corpus (5)

• "Peireles Substitution" and Chern-Simons Quantum Mechanics
• Geometric Gravitational Forces on Particles Moving in a Line
• Charged particle trajectories in a toroidal magnetic and rotation-induced electric field around a black hole
• Adiabatic Motion of a Quantum Particle in a Two-Dimensional Magnetic Field
• Non-minimal couplings in two dimensional gravity: a quantum investigation