Charged Particles in a 2+1 Curved Background

TL;DR

This paper analyzes the quantum behavior of charged particles in a 2+1 curved spacetime under strong magnetic fields, revealing a natural expansion and complex couplings influenced by geometry and spin.

Contribution

It introduces a novel expansion method for quantized charged particles in curved backgrounds and explores their geometric and spin interactions.

Findings

Second-order solutions for fast freedoms

Effective phase space parameterization

Coupling of slow Hamiltonian with curvature and spin-connection

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.