Higher-Order Differential Operators on a Lie Group and Quantization

This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or representations of Lie groups in those anomalous cases where the Kostant-Kirilov co-adjoint method or the Borel-Weyl-Bott representation algorithm do not succeed.Comment: 9 pages, latex, no figures, uses IJMPB.sty (included). New version partially rewritten (title changed!), presented to the II Int. Workshop on Class. and Quant. Integrable Systems, Dubna (Rusia) 1996, and published in Int. J. Mod. Phys.

Hermite Coherent States for Quadratic Refractive Index Optical Media

Producción CientíficaLadder and shift operators are determined for the set of Hermite–Gaussian modes associated with an optical medium with quadratic refractive index profile. These operators allow to establish irreducible representations of the su(1, 1) and su(2) algebras. Glauber coherent states, as well as su(1, 1) and su(2) generalized coherent states, were constructed as solutions of differential equations admitting separation of variables. The dynamics of these coherent states along the optical axis is also evaluated.MINECO grant MTM2014-57129-C2-1-P and Junta de Castilla y Leon grant VA057U16