Gravitational anyonization

Publisher Website
Google Scholar
Abstract
The statistics of scalar matter changes when it is coupled to a U(1) gauge field with Chern-Simons dynamics, because all particles carry a magnetic flux and therefore give rise to Aharonov-Bohm phases when they move around each other. We argue that also the ‘‘dual’’ version of the Aharonov-Bohm effect, the Aharonov-Casher effect, can give rise to Berry phases which transmute ordinary particles into anyons. The Aharonov-Casher effect consists of an extra topological phase in the wave function of a magnetic moment moving around an electric charge. Considering (2+1)-dimensional Dirac fermions at low energies, both effects are present, and the fermions are turned into (interacting) anyons even though there is no Chern-Simons term included in the action. We study in detail the gravitational analogue of this mechanism. The post-Newtonian approximation is applied to the gravitational interaction of (2+1)-dimensional particles with spin, and to stringlike matter distributions with internal angular momentum in 3+1 dimensions. The action for gravity is taken to be the pure Einstein-Hilbert term. In the adiabatic limit one finds scrA⋅v-type interactions where scrA is a long-range vortex field. These interactions give rise to various kinds of Berry phases, in particular to the gravitational analogues of the Aharonov-Bohm and the Aharonov-Casher phases. The former occurs when a mass moves around a particle with spin, and the latter arises when a particle with spin moves in the Newtonian scalar potential of a second (spinless) particle. These Berry phases lead to a ‘‘self-anyonization’’ of particles with nonzero spin. The topological term in their effective action has the same structure as the one which obtains when spinless particles are considered, but with a gravitational Chern-Simons term included in the action for the gravitational field.