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Title: Abelian Chern-Simons vortices and holomorphic Burgers hierarchy
Authors: Pashaev, Oktay
Gürkan, Zeynep Nilhan
Keywords: Burgers hierarchy
Chern-Simons gauge theory
Holomorphic equation
Ishimori model
Kampe de Feriet polynomial
Noncommutative vortex
Issue Date: Jul-2007
Publisher: Pleiades Publishing
Source: Pashaev, O., and Gürkan, Z. N. (2007). Abelian Chern-Simons vortices and holomorphic Burgers hierarchy. Theoretical and Mathematical Physics, 152(1), 1017-1029. doi:10.1007/s11232-007-0086-0
Abstract: We consider the Abelian Chern-Simons gauge field theory in 2+1 dimensions and its relation to the holomorphic Burgers hierarchy. We show that the relation between the complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics has the meaning of the analytic Cole-Hopf transformation, linearizing the Burgers hierarchy and transforming it into the holomorphic Schrödinger hierarchy. The motion of planar vortices in Chern-Simons theory, which appear as pole singularities of the gauge field, then corresponds to the motion of zeros of the hierarchy. We use boost transformations of the complex Galilei group of the hierarchy to construct a rich set of exact solutions describing the integrable dynamics of planar vortices and vortex lattices in terms of generalized Kampe de Feriet and Hermite polynomials. We apply the results to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing the dynamics of magnetic vortices and the corresponding lattices in terms of complexified Calogero-Moser models. We find corrections (in terms of Airy functions) to the two-vortex dynamics from the Moyal space-time noncommutativity.
ISSN: 0040-5779
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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