In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature‐invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature‐invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross‐relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl‐Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro‐magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov‐Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Geometrically Induced Interactions and Bifurcations
SPACE, PROPULSION & ENERGY SCIENCES INTERNATIONAL FORMUM SPESIF‐2010: 14th Conference on Thermophysics Applications in Microgravity 7th Symposium on New Frontiers in Space Propulsion Sciences 2nd Symposium on Astrosociology 1st Symposium on High Frequency Gravitational Waves ; 2010 ; Huntsville (Alabama)
AIP Conference Proceedings ; 1208 , 1 ; 192-206
2010-01-28
15 pages
Conference paper
Electronic Resource
English
Modal Interactions in a Geometrically Nonlinear Cantilevered Beam
British Library Conference Proceedings | 2011
|Semiconductor Laser Bifurcations
British Library Conference Proceedings | 1996
|