{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T20:40:03Z","timestamp":1723063203305},"reference-count":0,"publisher":"Wiley","issue":"69","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>We introduce and discuss the generalized Klein\u2010Gordon second\u2010order\npartial differential equation in the Robertson\u2010Walker space\u2010time,\nusing the Casimir second\u2010order invariant operator written in\nhyperspherical coordinates. The de Sitter and anti\u2010de Sitter\nspace\u2010times are recovered by means of a convenient choice of the\nparameter associated to the space\u2010time curvature. As an\napplication, we discuss a few properties of the solutions. We also\ndiscuss the case where we have positive frequency exponentials and\nthe creation and annihilation operators of particles with known\nquantum numbers. Finally, we recover the Minkowskian case, that\nis, the case of null curvature.<\/jats:p>","DOI":"10.1155\/s0161171204406565","type":"journal-article","created":{"date-parts":[[2004,12,23]],"date-time":"2004-12-23T07:44:21Z","timestamp":1103787861000},"page":"3775-3781","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The second\u2010order Klein\u2010Gordon field equation"],"prefix":"10.1155","volume":"2004","author":[{"given":"D.","family":"Gomes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. Capelas","family":"De Oliveira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,12,23]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/710864.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204406565","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T19:45:31Z","timestamp":1723059931000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204406565"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"69","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204406565"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204406565","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2004-06-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-12-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}