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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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 41–54, 1989.
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Karasev, M.V. Connections on Lagrangian submanifolds and some quasiclassical approximation problems. I. J Math Sci 59, 1053–1062 (1992). https://doi.org/10.1007/BF01480686
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DOI: https://doi.org/10.1007/BF01480686