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We briefly review the theoretical formulations and applications of theAharonov--Bohm effect and the Aharonov--Casher effect with emphasis onmesoscopic physics. Topics relating to the Aharonov--Bohm effect include:locality, periodicity, non-integrable phase factors, Abelian gauge theory,interference, the spectrum and persistent current of electrons on a ringpierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohminterferometer. Topics relating to the Aharonov--Casher effect include: amagnetic dipole in an electric field, locality, periodicity, non-Abelian gaugeinvariance, SU(2) non-integrable phase factors, spin-orbit coupling, Pauliequation, Rashba Hamiltonian, Aharonov--Casher interferometer, conductance andpolarization in two-channel systems due to the Aharonov--Casher effect.

Aharonov--Bohm and Aharonov--Casher effects in meso-scopic physics: A brief review