Noncommutative solitons on Kähler manifolds

We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kähler manifold by using Berezin’s geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/h̄ correction to the soliton energy and for homogeneous Kähler manifolds obtain that the stable solitons are given in terms of generalized coherent states. We apply this general formalism to a number of examples, which include the sphere, hyperbolic plane, torus and general symmetric bounded domains. As a general feature we notice that on homogeneous manifolds of positive curvature, solitons tend to attract each other, while if the curvature is negative they will repel each other. Applications of these results are discussed. June 2001 1 On leave from L. D. Landau Institute for Theoretical Physics, Moscow, Russia. [email protected], [email protected]