On informational completeness of covariant localization observables and Wigner coefficients

DOI10.1063/1.531318zbMath0839.43012OpenAlexW2047376391MaRDI QIDQ4837364

Franklin E. jun. Schroeck, Dennis M. jun. Healy

Publication date: 16 June 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531318

zbMATH Keywords

homogeneous spacesHeisenberg groupunitary representationsLie algebrascoadjoint orbitsquantum mechanicsnilpotent Lie groupscompact groupsStone-von Neumann theoremsquare integrable representationslocally compact topological groupWigner distributionslocally compact topological groupsirreducible linear representationsquantum holographyGalilean groupsphysical astronomy

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Unitary representations of locally compact groups (22D10) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Compact groups (22C05)

Related Items (13)

Localization of the photon on phase space ⋮ SQUARE INTEGRABLE PROJECTIVE REPRESENTATIONS AND SQUARE INTEGRABLE REPRESENTATIONS MODULO A RELATIVELY CENTRAL SUBGROUP ⋮ Further results on the observability of quantum systems under general measurement ⋮ Some properties of transforms in cultural theory ⋮ Towards a classification of incomplete Gabor POVMs in ℂ ^d ⋮ Remarks on resolutions of Hilbert–Schmidt operators ⋮ Phase space observables and isotypic spaces ⋮ The Lorentz-Dirac equation in complex space-time ⋮ An algebra of effects in the formalism of quantum mechanics on phase space ⋮ Algebra of effects in the formalism of quantum mechanics on phase space as an M. V. and a Heyting effect algebra ⋮ Perspectives: Quantum mechanics on phase space ⋮ A general theorem on square-integrability: Vector coherent states ⋮ Characterization of informational completeness for covariant phase space observables

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