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

V. I. Skripnik

Institute of Mathematics, 3, Tereshchenko str. 252601, Kyiv, Ukraine

Abstract: 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).

Received: 22.05.1995

Language: English

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