THOMAS PRECESSION, BERRY POTENTIAL, AND THE MERON

The Thomas precession in the nonrelativistic limit of the Dirac equati on may be attributed to a non-Abelian Berry vector potential. We ask w hat object produces the non-Abelian potential in parameter space, in t he same sense that the Abelian vector potential arising in the adiabat ic transport of a nondegenerate level is produced by a monopole (cente red at the point where the level becomes degenerate with another) as s hown By Berry. We find that it is a meron, an object in four Euclidean dimensions with instanton number 1/2, centered at the point where the doubly degenerate positive and negative energy levels of the Dirac eq uation become fourfold degenerate.