Quantization in singular real polarizations: K "ahler regularization,\n Maslov correction and pairings

2014/12/31 by João N. Esteves, Esteves, João N., José M. Mourão +3
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics #Atomic and Subatomic Physics Research

paper · pdf · doi:10.48550/arxiv.1501.00112

Abstract

We study the Maslov correction to semiclassical states by using a K "ahler\nregularized BKS pairing map from the energy representation to the Schr "odinger\nrepresentation. For general semiclassical states, the existence of this\nregularization is based on recently found families of K "ahler polarizations\ndegenerating to singular real polarizations and corresponding to special\ngeodesic rays in the space of K "ahler metrics. In the case of the\none-dimensional harmonic oscillator, we show that the correct phases associated\nwith caustic points of the projection of the Lagrangian curves to the\nconfiguration space are correctly reproduced.\n

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