Gaussian curvature and global effects: Gravitational Aharonov-Bohm effect revisited

Abstract

Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by Ford and Vilenkin in the linearized regime.Employing the 1+3 formulation of spacetime decomposition we study the same effect in the context of full Einstein field equations for stationary spacetimes. Applying our approach to static tube-like and cylindrical distributions of dust not only we recover their result but also obtain an extra term which is interpreted to be representing the classical version of the Colella-Overhauser-Werner effect (the COW experiment). * Electronic address: nouri@khayam.ut.ac.ir, corresponding author † Electronic address: a.parvizi@ut.ac.ir

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

“…The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15,16], δ-like singularities [17][18][19], supersymmetry [20,21], condensed matter [22,23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28][29][30], black hole [31,32] and noncommutative theories [33,34].…”

“…In Sec. 4 we apply the method for the spin-1/2 AB problem plus a two-dimensional isotropic harmonic oscillator. We derive the expression for the particle energy spectrum and analyze it in the limit case of the vanishing harmonic oscillator potential recasting the result of usual spin-1/2 AB problem in conical space.…”

“…The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15, 16], δ-like singularities [17-19], supersymmetry [20, 21], condensed matter [22, 23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28-30], black hole [31, 32] and noncommutative theories [33, 34].In the AB effect of spin-1/2 particles [7], besides the interaction with the magnetic potential, an additional two dimensional δ-function appears as the mathematical description of the Zeeman interaction between the spin and the magnetic flux tube [18,19]. This interaction is the basis of the spin-orbit coupling, which causes a splitting on the energy spectrum of atoms depending on the spin state.…”

Optical Aharonov–Bohm effect due to toroidal moment inspired by general relativity

“…Different versions of gravitational analogue of the Aharonov-Bohm effect are discussed in the literature all of which corresponding to a test particle moving in a region of space in which either the gravitomagnetic field (  B g ) or the gravitoelectric field (  E g ) are absent, but the particle is affected by the fluxes of the same fields in the regions of spacetime from which it is excluded [26]. These two versions could be called gravitomagnetoic and gravitoelectric Aharonov-Bohm effects respectively [27]. Obviously the gravitomagnetic Aharonov-Bohm effect is more analogous, specially in its form, to its electromagnetic counterpart which involves magnetic field and its potential.…”

Relativistic quantum dynamics of vector bosons in an Aharonov–Bohm potential

“…The first case is when the spin projection s 3 = 0. In this case the Pauli term is absent and the radial operator O becomes O 0 and f (3) m can be expressed as a solution of the modified Bessel differential equation. We can see that the system does not admit boundstate solutions.…”