Geometric phases can be observed by interference as preferred scattering directions in the Aharonov-Bohm (AB) effect or as Berry phase shifts leading to precession on cyclic paths. Without curvature single-valuedness is lost in both case. It is shown how the deficit angle of the AB conic metric and the geometric precession cone vertex angle of the Berry phase can be adjusted to restore single-valuedness. The resulting interplay between both phases confirms the non--linear iterative system providing for generalized fine structure constants (...) obtained in the preliminary work. Topological solitons of the scalar coupling field emerge as localized, non-dispersive and non-singular solutions of the (complex) sine-Gordon equation with a relation to the Thirring coupling constant and non-linear optics. (shrink)

In this paper it is shown how higher-dimensional solitons can be stabilized by a topological phase gradient, a field-induced shift in effective dimensionality. As a prototype, two instable 2-dimensional radial symmetric Sine-Gordon extensions (pulsons) are coupled by a sink/source term such, that one becomes a stable 1d and the other a 3d wave equation. The corresponding physical process is identified as a polarization that fits perfectly to preliminary considerations regarding the nature of electric charge and background of 1/137. The coupling (...) is iterative with convergence limit and bifurcation at high charge. It is driven by the topological phase gradient or non-local Gauge potential that can be mapped to a local oscillator potential under PSL(2,R). (shrink)

Previous results have shown that the linear topological potential-to-phase relationship (well known from Josephson junctions) is the key to iterative coupling and non-perturbative bosonization of the 2 two-spinor Dirac equation. In this paper those results are combined to approach the nature of proton, neutron, and electron via extrapolations from the Planck scale to the System of Units (SI). The electron acts as a bosonizing bridge between opposite parity topological currents. The resulting potentials and masses are based on a fundamental soliton (...) mass limit and two iteratively obtained coupling constants, where one is the fine structure constant. The simple non-perturbative and relativistic results are within measurement uncertainty and show a very high significance. The deviation for the proton and electron masses are approximately 1 ppb (10^-9), for the neutron 4 ppb. (shrink)

Solitons can be well described by the Lagrange formalism of effective field theories. But usually mass and coupling constants constitute phenomenological dimensions without any relation to the topological processes. This paper starts with a two-spinor Dirac equation in radial symmetry including vector Coulomb and scalar Lorentz potentials, and arrives after bosonization at the sine-Gordon equation. The keys of non-perturbative bosonization are in this case topological phase gradients (topological currents) that can be balanced in iterative processes providing for coupling constants driven (...) by phase averaging and ``noise reduction'' in closed-loops and autoparametric resonance. A fundamental iterative spin-parity-asymmetry and dimensional shift quite near to the electron to proton mass ratio is found that can only be balanced by bosonization including Coulomb interaction. (shrink)