Topological Phase Fields, Baecklund Transformations, and Fine Structure

Binder, Bernd (2002) Topological Phase Fields, Baecklund Transformations, and Fine Structure.

Abstract

Quantum coupling is defined by comparing the evolution of an input
to an output phase, where the phase is evolving on a curved
pseudospherical surface. The difference given by interference
obeys a single-valuedness condition since the output phase is
coupling back to the input phase. We arrive at B\"acklund
transforms and corresponding sine-Gordon soliton equation. The
idealized resonance or feedback condition corresponds to an
oscillator potential that can be mapped by projective geometry to
Coulomb coupling, where the effective coupling strength can be
iteratively determined.