Se p 19 99 Complexification of Bohr - Sommerfeld conditions .
نویسنده
چکیده
The complex version of Bohr-Sommerfeld conditions is proposed. The BPU-construction (see [BPU] or [T1]) is generalized to this complexification. The new feature of this generalization is a spectral curve. The geometry of such curves is investigated. 1 Global structures on subspaces of Lagrangian cycles Let (M,ω) be a smooth symplectic manifold of dimesion 2n. It can be considered as a phase space of a classical mechanical system. The lagrangian submanifolds play an especially important role in symplectic geometry. Let L be a smooth manifold of dimension n and i : L → M (1.1) be an embedding of L into M . Then we can consider the subcycle i(L) ⊂ M as an orbit in the space Map(L,M) of smooth maps to M with respect to the natural action of the diffeomorphisms group Diff(L): (L ⊂ M) = Map(L,M)/Diff(L). (1.2) Such a submanifold is called Lagrangian if i(ω) = 0. (1.3)
منابع مشابه
Bohr-sommerfeld Star Products
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