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We apply the adiabatic approximation to investigate the low energy dynamicsof vortices in the parity invariant double self-dual Higgs model with onlymutual Chern-Simons interaction. When distances between solitons are large theyare particles subject to the mutual interaction. The dual formulation of themodel is derived to explain the sign of the statistical interaction. Whenvortices of different types pass one through another they behave like chargedparticles in magnetic field. They can form a bound state due to the mutualmagnetic trapping. Vortices of the same type exhibit no statisticalinteraction. Their short range interactions are analysed. Possible quantumeffects due to the finite width of vortices are discussed.Comment: keywords: vortex, vortices, anyons, fractional statistics, 20 pages  in Latex, accepted for publication in Phys.Rev.D, ( the above keywords  missing in the title were added

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Low energy dynamics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="normal">U</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>Chern-Simons solitons

Low energy dynamics of[U(1)]NChern-Simons solitons