02-408 Bernd Binder

Charge as the Stereographic Projection of Geometric Precession on Pseudospheres (58K, LaTeX 2e with 2 PS Figures) Sep 30, 02

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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 $PSL(2,{\Bbb R})$ 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.

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