Integrability of the Yang-Mills Hamiltonian system

Details Integrability of the Yang-Mills Hamiltonian system Integrability of the Yang-Mills Hamiltonian system

Apr 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..58..387k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 58, no. 4, p. 387-391

Mathematics

Dynamical Systems

5

Hamiltonian Functions, Numerical Integration, Yang-Mills Fields, Dynamical Systems, Gravitational Fields

Scientific paper

This paper considers the integrability of generalized Yang-Mills system with the Hamiltonian Ha(p,q) = 1/2 (p2 1 + p22 + a1q2 1 + a2q22) + 1/4q4 1 + 1/4a3q4 2 +1/2 a4q2 1q(exp2) 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 Painleve property. Therefore the Painleve test does not take account of the integrability for the case C.

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