Charge as the Stereographic Projection of Geometric Precession on Pseudospheres

Binder, Bernd (2002) Charge as the Stereographic Projection of Geometric Precession on Pseudospheres.

Abstract

In this paper geometric phases (Berry and Aharonov-Bohm) are generalized
to nonlinear topological phase fields on pseudospheres, where the
coordinate vector field is parallel transported along the
signal/soliton vector field with Levi--Civita connection.
Projective PSL(2,R} symmetry describes the relativistic
self-interacting bosonic sine-Gordon field. A Coulomb potential
can be induced as the stereographic projection of a harmonic
oscillator potential mapping angles or phases to distances and
vice versa resulting in mutual coupling with a generalized
coupling constant given by a nonlinear iteration. With
single-valuedness requirement in 137-gonal symmetry it fits within
a few ppb uncertainty to the Sommerfeld fine structure constant.