Research PaperNo Access

Classical limits of Hilbert bimodules as symplectic dual pairs

Benjamin H. Feintzeig

https://orcid.org/0000-0001-7692-5155

Department of Philosophy, University of Washington, Seattle, WA 98195-3350, USA

E-mail Address: bfeintze@uw.edu

Corresponding author.

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and

Jer Steeger

https://orcid.org/0000-0003-2771-4145

Department of Philosophy, University of Bristol, Bristol, BS6 6JL, UK

E-mail Address: jer.steeger@bristol.ac.uk

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https://doi.org/10.1142/S0129055X24500260Cited by:0 (Source: Crossref)

Abstract

Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic structures of the relevant types of models. Previously, it has been shown that one can functorially associate certain symplectic dual pairs to Hilbert bimodules through strict deformation quantization. We show that, in the inverse direction, strict deformation quantization also allows one to functorially take the classical limit of a Hilbert bimodule to reconstruct a symplectic dual pair.

Keywords:

AMSC: 17B63, 46L65, 81R10, 81S99

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