3 O ct 1 99 9 Canonical Reduction of Symplectic Structures for the Maxwell and Yang - Mills Equations . Part 1
نویسندگان
چکیده
The canonical reduction algorithm is applied to Maxwell and Yang-Mills equations considered as Hamiltonian systems on some fiber bundles with symplectic and connection structures. The minimum interaction principle proved to have geometric origin within the reduction method devised. 0. Preliminaries We begin by reviewing the backgrounds of the reduction theory subject to Hamiltonian systems with symmetry on principle fiber bundles. The material is partly available in [1,4], so here will be only sketched but in notation suitable for us. Let G denote a given Lie group with the unity element e ∈ G and the corresponding Lie algebra G ≃ T e (G). Consider a principal fiber bundle p : On the principal fiber bundle p : (M, ϕ) → N there is assigned a connection Γ(A) by means of such a morphism A:(T (M), ϕ g *) → (G, Ad), that for each u ∈ M a mapping A(u) : T u (M) → G is a left inverse one to the mappingû
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