Magnetic Translation Group. II. Irreducible Representations

The physical irreducible representations of the magnetic translation group (M.T.G.) defined previously have been found. From these a set of solutions of Schrödinger's equation for a Bloch electron in a magnetic field has been constructed. In general the M.T.G. is non-Abelian. However, when the magnetic flux through areas enclosed by any vectors of the Bravais lattice become multiples of an elementary "fluxon" $\frac{\mathrm{hc}}{e}$, the M.T.G. becomes isomorphic to the usual translation group.