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Open Quantum Systems Decoherence
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A Phase Space Representation of the Metaplectic Group
arXiv
Authors: Maurice de Gosson
Year
2025
Paper ID
36468
Status
Preprint
Abstract Read
~2 min
Abstract Words
80
Citations
N/A
Abstract
The symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space. We will construct an extension Mp(n) of Mp(n) acting on square integrable functions on phase space. This is performed using previous results of ours involving explicit expressions of the twisted Weyl symbols of metaplectic operators and Bopp pseudodifferential operators, which are phase space extensions of the usual Weyl operators.
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- The symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space.
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