On quantum systems of particles with singular magnetic interaction in one dimension. $\mathrm{M}$–$\mathrm{B}$ statistics

Quantum one-dimensional systems of particles interacting via singular “collective” (depending on all the position vectors of particles) vector electromagnetic potential is considered in a thermodynamic limit. The reduced density matrices in the limit are computed for the cases short-range interaction and one-dimensional analog of the Chern–Simons interaction the $j$-th “collective” vector electromagnetic potential of $n$ particles equals the partial derivative in the position vector of the $j$-th particle of the Coulomb potential energy of a system of $n$ charged particles).