Fourier transform and sigma model solitons on noncommutative tori (Q2192898)

The noncommutative solitons are stable maps of the Euler-Lagrange equation for a suitable energy functional defined on maps from a noncommutative torus, a source space modeling a string world sheet, to a target space made of two points, or the simplest nonlinear sigma model in noncommutative geometry. The known methods to find solitons depend on the existence of holomorphic structures for projective modules over a noncommutative torus. The construction of projective modules over a noncommutative torus relies on a general approach using the Schrödinger representation on a phase space. On the other hand, the Schrödinger representation on a lattice of the phase space has been used in a time-frequency analysis, so called Gabor analysis. In the paper under review, the dual Schrödinger representation which is unitarily equivalent to the Schrödinger representation, and thereby the dual bimodule of the Heisenberg bimodule with application to noncommutative solitons in mind are presented. This is done by methods of the Fourier transform.