{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T02:45:04Z","timestamp":1777689904777,"version":"3.51.4"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. Math. Phys."],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p> We show that the cross Wigner function can be written in the form [Formula: see text] where [Formula: see text] is the Fourier transform of \u03d5 and \u015c is a metaplectic operator that projects onto a linear symplectomorphism S consisting of a rotation along an ellipse in phase space (or in the time-frequency space). This formulation can be extended to generic Weyl symbols and yields an interesting fractional generalization of the Weyl\u2013Wigner formalism. It also provides a suitable approach to study the Bopp phase space representation of quantum mechanics, familiar from deformation quantization. Using the \"metaplectic formulation\" of the Wigner transform, we construct a complete set of intertwiners relating the Weyl and the Bopp pseudo-differential operators. This is an important result that allows us to prove the spectral and dynamical equivalence of the Schr\u00f6dinger and the Bopp representations of quantum mechanics. <\/jats:p>","DOI":"10.1142\/s0129055x13430101","type":"journal-article","created":{"date-parts":[[2013,11,10]],"date-time":"2013-11-10T21:08:45Z","timestamp":1384117725000},"page":"1343010","source":"Crossref","is-referenced-by-count":8,"title":["METAPLECTIC FORMULATION OF THE WIGNER TRANSFORM AND APPLICATIONS"],"prefix":"10.1142","volume":"25","author":[{"given":"NUNO COSTA","family":"DIAS","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa, Portugal"},{"name":"Grupo de F\u00edsica Matem\u00e1tica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"}]},{"given":"MAURICE A.","family":"DE GOSSON","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Wien, Fakult\u00e4t f\u00fcr Mathematik\u2013NuHAG, Nordbergstrasse 15, 1090 Vienna, Austria"}]},{"given":"JO\u00c3O NUNO","family":"PRATA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa, Portugal"},{"name":"Grupo de F\u00edsica Matem\u00e1tica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2013,12,10]]},"reference":[{"key":"rf1","first-page":"111","volume":"110","author":"Bayen F.","journal-title":"Ann. Phys."},{"key":"rf2","first-page":"6","volume":"111","author":"Bayen F.","journal-title":"Ann. 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