Abstract
Let $\mathsf{G}$ be a locally compact group satisfying some technical requirements and $\widehat{\sf{G}}$ its unitary dual. Using the theory of twisted crossed product $C^{*}$-algebras, we develop a twisted global quantization for symbols defined on $\mathsf{G}\times\widehat{\sf{G}}$ and taking operator values. The emphasis is on the representation-theoretic aspect. For nilpotent Lie groups, the connection is made with a scalar quantization of the cotangent bundle $T^{*}(\mathsf{G})$ and with a Quantum Mechanical theory of observables in the presence of variable magnetic fields.
Citation
H. Bustos. M. Măntoiu. "Twisted pseudo-differential operator on type I locally compact groups." Illinois J. Math. 60 (2) 365 - 390, Summer 2016. https://doi.org/10.1215/ijm/1499760013
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