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Maslov indices, Poisson brackets, and singular differential forms

Abstract : Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the $6j$-symbol, which is important in angular momentum theory and in quantum gravity.
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Submitted on : Wednesday, June 18, 2014 - 3:09:56 PM
Last modification on : Tuesday, October 19, 2021 - 10:48:21 PM

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Ilya Esterlis, Hal M. Haggard, Austin Hedeman, Robert G. Littlejohn. Maslov indices, Poisson brackets, and singular differential forms. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2014, 106, pp.50002. ⟨10.1209/0295-5075/106/50002⟩. ⟨hal-01009724⟩

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