Gauge Invariant Magnetism

Abstract

An introduction is given to features of gauge invariance in classical and quantum mechanics that are of importance for magnetism in condensed matter systems. A version of quantum mechanics is described in which full electromagnetic gauge arbitrariness is displayed explicitly at every stage. The division of orbital magnetism into paramagnetism and diamagnetism is examined and it is shown that only by treating both of these on an equal footing can a gauge invariant treatment of magnetism be constructed.