Fourier transform and sigma model solitons on noncommutative tori

Abstract

We investigate how Fourier transform is involved in the analysis of a twisted group algebra $$L^1(G, \sigma )$$ for $$G={\widehat{\Gamma }}\times \Gamma$$ and $$\sigma :G\times G \rightarrow \mathbb {T}$$ 2-cocycle where $$\Gamma$$ is a locally compact abelian group and $${\widehat{\Gamma }}$$ its Pontryagin dual related to noncommutative tori. We construct the dual Schrodinger representation which is unitarily equivalent to the Schrodinger representation, and thereby the dual bimodule of the Heisenberg bimodule with the application to noncommutative solitons in mind.