Gauge Theory Solitons on the Noncommutative Cylinder

The solution-generating technique originally suggested for gauge theories on the noncommutative plane is generalized to the noncommutative cylinder. For this, we construct partial isometry operators and a complete set of orthogonal projection operators in the algebra ${\mathcal A}_{\text{\rm C}}$ of the cylinder, and an isomorphism between the free module ${\mathcal A}_{\text{\rm C}}$ and its direct sum ${\mathcal A}_{\text{\rm C}}\oplus{\mathcal F}_{\text{\rm C}}$ with the Fock module on the cylinder. We explicitly construct the gauge theory soliton and evaluate the spectrum of perturbations about this soliton.