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A universal phase space for particles in Yang-Mills fields. (English) Zbl 0388.58010


MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37N99 Applications of dynamical systems
70H99 Hamiltonian and Lagrangian mechanics
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References:

[1] AbrahamR. and MarsdenJ., Foundations of Mechanics, 2nd edition, Benjamin/Cummings, Reading, Mass., 1978.
[2] ArnoldV.I., ?Mathematical Methods of Classical Mechanics?, Graduate Texts in Math., Vol. 60, Springer-Verlag, New York, 1978.
[3] Guillemin, V. and Sternberg, S., ?On the Equations of Motion of a Classical Particle in a Yang-Mills Field and the Principle of General Covariance?, to appear. · Zbl 0449.53051
[4] Kazhdan, D., Kostant, B., and Sternberg, S., ?Hamiltonian Group Actions and Dynamical Systems of Calogero Type?, Comm. Pure Appl. Math., to appear. · Zbl 0368.58008
[5] MarsdenJ. and WeinsteinA., ?Reduction of Symplectic Manifolds with Symmetry?, Reports on Math. Phys. 5, 121-130 (1974). · Zbl 0327.58005
[6] Sternberg, S., ?Minimal Coupling and the Symplectic Mechanics of a Classical Particle in the Presence of a Yang-Mills Field, Proc. Nat. Acad. Sci. U.S.A. (1977). · Zbl 0765.58010
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