Chern-Simons correlations on (2+1)D lattice

The contribution of zero modes to the value of the number of particles in a discrete model of the (2+1)-dimensional nonlinear Schrödinger equation is computed. It is shown for the first time that in the region of small values of the Chern-Simons coefficient k there exists a universal attraction between field configurations. For k=2 this phenomenon may be a dynamic origin of the semion pairing in the high-temperature superconducting state of planar systems. The preliminary results of this paper were presented in the proceedings of the XI International Conference on Problems of Quantum Field Theory (Dubna, 13–17 July 1998).