Berezin-Type Operators on the Cotangent Bundle of a Nilpotent Group

2019/05/07 by M. Mantoiu, Mantoiu, M.
Mathematics · #22E25 #22E45 #46L65 (Secundary) #47G30 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:22E25 #msc:22E45 #msc:46L65 #msc:47G30

paper · pdf · doi:10.48550/arxiv.1905.02837

21 pages

arxiv created 2019/05/07 · arxiv updated 2019/05/09

Abstract

We define and study coherent states, a Berezin-Toeplitz quantization and covariant symbols on the product between a connected simply connected nilpotent Lie group and the dual of its Lie algebra. The starting point is a Weyl system codifying the natural Canonical Commutation Relations of the system. The formalism is meant to complement the quantization of the cotangent bundle by pseudo-differential operators, to which it is connected in an explicit way. Some extensions are indicated, concerning τ-quantizations and variable magnetic fields.

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