Some Notes concerning the Dynamics of Noncommutative Solitons in the M(atrix) Theory as Well as in the Noncommutative Yang–mills Model

We consider a pair of noncommutative solitons in the noncommutative Yang–Mills/M(atrix) model. In the case when the solitons are separated by a finite distance their “polarisations” do not belong to orthogonal subspaces of the Hilbert space. In this case the interaction between solitons is nontrivial. We analyse the dynamics arisen due to this interaction in both naive approach of rigid solitons and exactly as described by the underlying gauge model. It appears that the exact description is given in terms of finite matrix models/multidimensional mechanics whose dimensionality depends on the initial conditions. The results are being generalised to the case of interacting solitons with arbitrary “polarisations”.