Frame transforms, star products and quantum mechanics on phase space

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dc.creatorAniello, P.
dc.creatorMan'ko, V. I.
dc.creatorMarmo, G.
dc.date2008-02-28
dc.date2008-04-10
dc.date.accessioned2026-07-07T11:40:32Z
dc.date.available2026-07-07T11:40:32Z
dc.descriptionUsing the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group $G\times G$. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed.
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/0802.4236
dc.identifierhttp://arxiv.org/abs/0802.4236
dc.identifierJ.Phys.A41:285304,2008
dc.identifierdoi:10.1088/1751-8113/41/28/285304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/200284
dc.subjectQuantum Physics
dc.titleFrame transforms, star products and quantum mechanics on phase space
dc.typetext

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