{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T19:09:32Z","timestamp":1649012972792},"reference-count":15,"publisher":"FapUNIFESP (SciELO)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["An. Acad. Bras. Ci\u00eanc."],"published-print":{"date-parts":[[2001,12]]},"abstract":"<jats:p>We study the behavior of massless Dirac particles, i.e., solutions of the Dirac equation with m = 0 in the presence of an electromagnetic field. Our main result (Theorem 1) is that for purely real or imaginary fields any Huygens type (in Hadamard's sense) Dirac operators is equivalent to the free Dirac operator, equivalence given by changes of variables and multiplication (right and left) by nonzero functions.<\/jats:p>","DOI":"10.1590\/s0001-37652001000400002","type":"journal-article","created":{"date-parts":[[2005,4,13]],"date-time":"2005-04-13T12:57:41Z","timestamp":1113397061000},"page":"483-493","source":"Crossref","is-referenced-by-count":0,"title":["On Huygens' principle for Dirac operators associated to electromagnetic fields"],"prefix":"10.1590","volume":"73","author":[{"given":"FABIO A.C.C.","family":"CHALUB","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica Pura e Aplicada,  Brazil"}]}],"member":"530","reference":[{"issue":"1","key":"ref1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.4171\/ZAA\/747","article-title":"A survey on Huygens' principle","volume":"16","author":"BELGER M","year":"1997","journal-title":"Z Anal Anwendungen"},{"issue":"6","key":"ref2","first-page":"7","article-title":"The Huygens principle and integrability","volume":"49","author":"BEREST Y","year":"1994","journal-title":"Uspekhi Mat Nauk"},{"issue":"2","key":"ref3","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1023\/A:1006069012474","article-title":"Hierarchies of Huygens' operators and Hadamard's conjecture","volume":"53","author":"BEREST Y","year":"1998","journal-title":"Acta Appl Math"},{"key":"ref4","series-title":"Eletromagnetic Theory of Propagation, Interference and Diffraction of Light","author":"BORN M","year":"1980","edition":"sixth"},{"key":"ref5","series-title":"Proceedings of the Workshop on Nonlinearity, Integrability and All That: Twenty Years after NEEDS '79 (Gallipoli, 1999)","first-page":"89","volume-title":"Integrable systems, Huygens' principle, and Dirac operators","author":"CHALUB FACC","year":"2000"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"62","DOI":"10.2991\/jnmp.2001.8.s.12","article-title":"On Huygens' Principle for Dirac Operators and Nonlinear Evolution Equations","volume":"8","author":"CHALUB FACC","year":"2001","journal-title":"J Nonlin Math Phys"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1098\/rspa.1928.0023","article-title":"The Quantum Theory of the Electron","volume":"117","author":"DIRAC PAM","year":"1928","journal-title":"Proc Roy Soc of London"},{"issue":"1","key":"ref8","first-page":"25","article-title":"Fundamental solutions for the wave operator","volume":"15","author":"FOLLAND GB","year":"1997","journal-title":"Exposition Math"},{"key":"ref9","series-title":"Clifford algebras and Dirac operators in harmonic analysis","author":"GILBERT JE","year":"1991"},{"key":"ref10","series-title":"Lectures on Cauchy's problem in linear partial differential equations","author":"HADAMARD J","year":"1953"},{"key":"ref11","series-title":"Trait\u00e9 de La Lumi\u00e9re, o\u00f9 sont expliqu\u00e9es les causes de ce qui luy-arrive dans la reflexion, et dans la refraction et particuli\u00e8rement dans l'etrange refraction du Cristal D'Islande","author":"HUYGENS C","year":"1920"},{"issue":"1","key":"ref12","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF03041932","article-title":"Dirac gamma-equation, classical gauge fields and Clifford algebra","volume":"8","author":"MARCHUK NG","year":"1998","journal-title":"Adv Appl Clifford Algebras"},{"key":"ref13","series-title":"Opticks: A treatise of the Reflexion, Inflexion and Colours of Light","author":"NEWTON I","year":"1979"},{"key":"ref14","series-title":"Advanced Quantum Mechanics","author":"SAKURAI JJ","year":"1967"},{"key":"ref15","series-title":"The Dirac equation","author":"THALLER B","year":"1992"}],"container-title":["Anais da Academia Brasileira de Ci\u00eancias"],"original-title":[],"link":[{"URL":"http:\/\/www.scielo.br\/pdf\/aabc\/v73n4\/v73n4a02.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,5,24]],"date-time":"2017-05-24T17:13:11Z","timestamp":1495645991000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.scielo.br\/scielo.php?script=sci_arttext&pid=S0001-37652001000400002&lng=en&tlng=en"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,12]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2001,12]]}},"alternative-id":["S0001-37652001000400002"],"URL":"https:\/\/doi.org\/10.1590\/s0001-37652001000400002","relation":{},"ISSN":["0001-3765"],"issn-type":[{"value":"0001-3765","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,12]]}}}