Abstract
In this paper we construct a flat connection (possibly with torsion) on Lagrangian submanifolds which is connected with formulas for asymptotic wave functions generated by this submanifold. The new formalism naturally includes the Bohr-Sommerfeld condition and Maslov characteristic class and lets us establish new global formulas for asymptotic wave functions in the subtlest cases (motion in the neighborhood of a separatrix).
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