On the integrability of the generalized Yang–Mills system

Volume 31 / 2004

A. Lesfari, A. Elachab Applicationes Mathematicae 31 (2004), 345-351 MSC: 70H05, 70H06, 14H70, 14H40. DOI: 10.4064/am31-3-8

Abstract

We consider a hamiltonian system which, in a special case and under the gauge group $SU(2)$, can be considered as a reduction of the Yang–Mills field equations. We prove explicitly, using the Lax spectral curve technique and the van Moerbeke–Mumford method, that the flows generated by the constants of motion are straight lines on the Jacobi variety of a genus two Riemann surface.

Authors

  • A. LesfariDepartment of Mathematics
    Faculty of Sciences
    University of Chouaïb Doukkali
    B.P. 20, El-Jadida, Morocco
    e-mail
    e-mail
  • A. ElachabDepartment of Mathematics
    Faculty of Sciences
    University of Chouaïb Doukkali
    B.P. 20, El-Jadida, Morocco.

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