{"id":241814,"date":"2016-07-11T02:00:00","date_gmt":"2016-07-10T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=c0ec6075f809463ee463e7c44ba0ef86"},"modified":"2016-07-11T02:00:00","modified_gmt":"2016-07-10T23:00:00","slug":"the-clifford-algebra-of-physical-space-and-dirac-theory","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=241814","title":{"rendered":"The Clifford algebra of physical space and Dirac theory"},"content":{"rendered":"<p>The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli<br \/>\nmatrices is shown to not be completely true. It is only true as long as the term ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/5\/055407\/ejpaa2c9bieqn1.gif] {$\\beta \\psi $} in the usual<br \/>\nDirac factorization of the Klein\u2013Gordon equation is assumed to be the product of a square matrix \u03b2<br \/>\nand a column matrix \u03c8 . In this paper we show that there is another possibility besides this matrix<br \/>\nproduct, in fact a possibility involving a matrix operation, and show that it leads to another<br \/>\npossible expression for the Dirac equation. We show that, behind this other possible factorization<br \/>\nis the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss<br \/>\nseveral different aspects of Dirac theory using this formalism. In particular, we show that there<br \/>\nare four different possible sets of definitions for the parity, time reversal, and cha&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli<br \/>\nmatrices is shown to not be completely true. It is only true as long as the term ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/5\/055407\/ejpaa2c9bieq&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-241814","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/241814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=241814"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/241814\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=241814"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=241814"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=241814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}