Supersymmetry and Integrability in Planar Mechanical Systems

Details Supersymmetry and Integrability in Planar Mechanical Systems Supersymmetry and Integrability in Planar Mechanical Systems

2005-04-26

arxiv.org/abs/hep-th/0504212v2

Int.J.Theor.Phys.46:2983-3004,2007

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 3 figures

Scientific paper

10.1007/s10773-007-9413-3

We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory with the assumption of spatially homogeneous field configurations and a particular ansatz imposed on the gauge potentials in the dimensional reduction procedure. The Painleve test is adopted to discuss integrability and we focus on the role of supersymmetry and parity invariance in two space dimensions for the attainment of integrable or chaotic models. Our conclusion is that the relationships among the parameters imposed by supersymmetry seem to drastically reduce the number of possibilities for integrable interaction potentials of the mechanical system under consideration.

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