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Berezin-type operators on the cotangent bundle of a nilpotent group

  • M. MăntoiuEmail author
Original Research

Abstract

We define and study coherent states, a Berezin–Toeplitz quantization and covariant symbols on the product \(\varXi \,{:}{=}\,{\mathsf {G}}\times \mathfrak {g}^\sharp \) 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 \(T^\sharp {\mathsf {G}}\cong {\mathsf {G}}\times \mathfrak {g}^\sharp \) by pseudo-differential operators, to which it is connected in an explicit way. Some extensions are indicated, concerning \(\tau \)-quantizations and variable magnetic fields.

Keywords

Nilpotent group Lie algebra Coherent states Pseudo-differential operator Symbol Berezin quantization 

Mathematics Subject Classification

Primary 22E25 47G30 Secondary 22E45 46L65 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Facultad de CienciasUniversidad de ChileNunoaChile

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