Fermion-solenoid interactions: Vacuum charge and scattering theory

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Abstract
Properties of the Dirac Hamiltonian for fermions in two space dimensions, interacting with a solenoid, are studied in the case of a finite solenoid radius and in the zero-radius limit. The asymmetric part of the Hamiltonian’s spectral density is explicitly expressed in terms of the fermion’s scattering phase shifts, and the convergence of the partial-wave expansion is examined. The spectral asymmetry, or equivalently the anomaly, is related to scattering amplitudes at high energy and can be easily evaluated using the eikonal approximation. A generalization to higher dimensions is briefly outlined.