Celestial Mechanics and Dynamical Astronomy

, Volume 58, Issue 4, pp 387–391 | Cite as

Integrability of the Yang-Mills Hamiltonian system

  • S. Kasperczuk


This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH a (p, q)=1/2(p 1 2 +p 2 2 +a1q 1 2 +a2q 2 2 )+1/4q 1 4 +1/4a3q 2 4 + 1/2a4q 1 2 q 2 2 . We prove that the system is integrable for the cases: (A)a1=a2,a3=a4=1; (b)a1=a2,a3=1,a4=3; (C)a1=a2/4,a3=16,a4=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.

Key words

Hamiltonian systems Painlevé test integrability 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • S. Kasperczuk
    • 1
  1. 1.Institute of PhysicsPedagogical UniversityZielona GóraPoland

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