For systems of particles with singular magnetic interation for special choice of a selfadjoint extension of the Hamiltoniam equilibrium reduced density matrices are calculated in the thermodynamic limit for simplest pair magnetic potentials.
Quantum systems of particles interacting via an effective electromagnetic potential with zero electrostatic component are considered (magnetic interaction). It is assumed that the j th component of the effective potential for n particles equals the partial derivative with respect to the coordinate of the jth particle of “magnetic potential energy” of n particles almost everywhere. The reduced density matrices for small values of the activity are computed in the thermodynamic limit for d-dimensional systems with short-range pair magnetic potentials and for one-dimensional systems with long-range pair magnetic interaction, which is an analog of the interaction of three-dimensional Chern-Simons electrodynamics (“magnetic potential energy” coincides with the one-dimensional Coulomb (electrostatic) potential energy).
Gibbs states and dynamics are described for systems of charged particles interacting via eective electromagnetic eld, characterized by a (singular) vector potential with zero electrostatic component(magnetic interaction).The mean{ eld type limit for the Gibbs (grand canonical) correlation functions for the 2-d Chern{Simons (CS) system (the vector potential of the n-particle system is a skew derivative of the Coulomb potential energy of the n-particle system) is performed.It is found that the limit is not unique.For 1-d quantum system of particles with Maxwell{Boltzmann statistics and analog of CS interaction ( the vector potential for the n-particle system is the derivative of the 1-d Coulomb potential energy of the system) the Gibbs reduced density matrices are found in the thermodynamic limit.It is shown that in 1-d systems singular interactions may produce anyonic statistics.