DOI: https://doi.org/10.30970/jps.01.317
ANYONS AND SYSTEMS OF PARTICLES WITH MAGNETIC INTERACTIONS IN THE THERMODYNAMIC LIMIT
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Journal of Physical Studies 1(3), 317–323 (1997)
DOI: https://doi.org/10.30970/jps.01.317 ANYONS AND SYSTEMS OF PARTICLES WITH MAGNETIC INTERACTIONS IN THE THERMODYNAMIC LIMIT |
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W. I. Skrypnik
Institute of Mathematics, 3 Tereshchenkivska Str., Kyiv, Ukraine
Gibbs states and dynamics are described for systems of charged particles interacting via effective electromagnetic field, characterized by a (singular) vector potential with zero electrostatic component(magnetic interaction). The mean-field 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.