Thomas Precession, Berry potential and the Meron

Details Thomas Precession, Berry potential and the Meron Thomas Precession, Berry potential and the Meron

1994-03-14

arxiv.org/abs/hep-th/9403076v1

Phys.Rev.Lett. 73 (1994) 1565-1569

Physics

High Energy Physics

High Energy Physics - Theory

14pages

Scientific paper

10.1103/PhysRevLett.73.1565

We begin with a prior observation by one of us that Thomas precession in the nonrelativistic limit of the Dirac equation may be attributed to a nonabelian Berry vector potential. We ask what object produces the nonabelian potential in parameter space, in the same sense that the abelian vector potential arising in the adiabatic transport of a nondegenerate level is produced by a monopole, (centered at the point where the level becomes degenerate with another), as shown by Berry. We find that it is a {\em meron}, an object in four euclidean dimensions with instanton number ${1 \over 2}$, centered at the point where the doubly degenerate positive and negative energy levels of the Dirac equation become fourfold degenerate.

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