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

Abstract

We define and study coherent states, a Berezin-Toeplitz quantization and covariant symbols on the product Xi := G x g(#) 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(#)G congruent to G x g(#) by pseudodifferential operators, to which it is connected in an explicit way. Some extensions are indicated, concerning tau-quantizations and variable magnetic fields.