The Spin Interaction of a Dirac Particle in an Aharonov-Bohm Potential in First Order Scattering

For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix is related to one of the generators of rotation in the spin space of the particle. This operator, which is given by the projection of the spin operator Σ along the direction of the total momentum of the system, and the two operators constructed from the projections of the Σ operator along the momentum transfer and the z-directions close the SU(2) algebra. It is suggested, then, that these two directions of the total momentum and the momentum transfer form some sort of natural intrinsic directions in terms of which the spin dynamics of the scattering process at first order can be formulated conveniently. A formulation and an interpretation of the conservation of helicity at first order using the spin projection operators along these directions is presented.     

Gravitational Aharonov-Bohm Effect

We study a purely gravitational Aharonov-Bohm effect. The space-time curvature is concentrated in the quasiregular singularity of a cosmic string, outside of which space-time is (locally) flat. The symmetries of this field configuration are described by the groupoid symmetries rather than by the usual group symmetries. The groupoid in question is formed by homotopy classes of piecewise smooth paths in the cosmic string region. A gravitational counterpart of the Aharonov-Bohm effect occurs if the symmetry of the system, with respect to the groupoid action, is broken down.     

Quark confinement and the fractional quantum Hall effect

Working in the physics of Wilson factor and Aharonov-Bohm effect, we find in the fluxtube-quark system the topology of a baryon consisting of three heavy flavor quarks resembles that of the fractional quantum Hall effect (FQHE) in condensed matter. This similarity yields the result that the constituent quarks of baryon have the ``filling factor' 1/3, thus the previous conjecture that quark confinement is a correlation effect is confirmed. Moreover, by deriving a Hamiltonian of the system analogous to that of FQHE, we predict an energy gap for the ground state of a heavy three-quark system.