{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T12:33:55Z","timestamp":1766493235179,"version":"3.41.2"},"reference-count":26,"publisher":"AIP Publishing","issue":"1","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"<jats:p>We study a transform, inspired by coherent state transforms, from the Hilbert space of Clifford algebra valued square integrable functions L2(\u211dm, dx) \u2297 \u2102m to a Hilbert space of solutions of the Weyl equation on \u211dm+1 = \u211d \u00d7 \u211dm, namely, to the Hilbert space \u2133L2(\u211dm+1, d\u03bc) of \u2102m-valued monogenic functions on \u211dm+1 which are L2 with respect to an appropriate measure d\u03bc. We prove that this transform is a unitary isomorphism of Hilbert spaces and that it is therefore an analog of the Segal-Bargmann transform for Clifford analysis. As a corollary, we obtain an orthonormal basis of monogenic functions on \u211dm+1. We also study the case when \u211dm is replaced by the m-torus \ud835\udd4bm. Quantum mechanically, this extension establishes the unitary equivalence of the Schr\u00f6dinger representation on M, for M = \u211dm and M = \ud835\udd4bm, with a representation on the Hilbert space \u2133L2(\u211d \u00d7 M, d\u03bc) of solutions of the Weyl equation on the space-time \u211d \u00d7 M.<\/jats:p>","DOI":"10.1063\/1.4974449","type":"journal-article","created":{"date-parts":[[2017,1,26]],"date-time":"2017-01-26T14:09:25Z","timestamp":1485439765000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":16,"title":["Coherent state transforms and the Weyl equation in Clifford analysis"],"prefix":"10.1063","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6834-4596","authenticated-orcid":false,"given":"Jos\u00e9","family":"Mour\u00e3o","sequence":"first","affiliation":[{"name":"University of Lisbon 1 Department of Mathematics and Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior T\u00e9cnico, , Lisbon, Portugal"}]},{"given":"Jo\u00e3o P.","family":"Nunes","sequence":"additional","affiliation":[{"name":"University of Lisbon 1 Department of Mathematics and Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior T\u00e9cnico, , Lisbon, Portugal"}]},{"given":"Tao","family":"Qian","sequence":"additional","affiliation":[{"name":"University of Macau 2 Department of Mathematics, Faculty of Science and Technology, , Macau, China"}]}],"member":"317","published-online":{"date-parts":[[2017,1,26]]},"reference":[{"key":"2023070203481643700_c1","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1002\/cpa.3160140303","article-title":"On a Hilbert space of analytic functions and an associated integral transform part I","volume":"14","year":"1961","journal-title":"Commun. 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