{"id":12154,"date":"2021-01-21T12:02:39","date_gmt":"2021-01-21T17:02:39","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12154"},"modified":"2021-01-21T12:02:39","modified_gmt":"2021-01-21T17:02:39","slug":"what-is-a-spinor","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12154","title":{"rendered":"What is a Spinor?"},"content":{"rendered":"<p>Recently Jean-Pierre Bourguignon recently gave the <a href=\"https:\/\/www.icms.org.uk\/events\/event\/?id=1128\">Inaugural Atiyah Lecture<\/a>, with the title <em>What is a Spinor?<\/em>   The title was a reference to a <a href=\"https:\/\/www.youtube.com\/watch?v=SBdW978Ii_E\">2013 talk by Atiyah at the IHES<\/a> with the same title.  Bourguignon&#8217;s lecture is not yet online, but I realized there are lectures explaining what a spinor is that I can highly recommend: <a href=\"https:\/\/www.youtube.com\/playlist?list=PLOaEOh8qMwDLeEdrwt3n8xLErYi9iQPY5\">my own, in this semester&#8217;s course on the mathemematics of quantum mechanics<\/a>.  I&#8217;m closely following the <a href=\"https:\/\/www.math.columbia.edu\/\/~woit\/QMbook\/qmbook-latest.pdf\">textbook I wrote<\/a>.<\/p>\n<p>Teaching this course this past academic year has made me all too aware of things that are less than ideal about the book, and I unfortunately haven&#8217;t had time to get to work on making any significant improvements.  Going through the material on spinors though, I&#8217;m pretty happy with how that part of the book turned out, think it provides a clear explanation of a beautiful and important story, one that is not readily available elsewhere.<\/p>\n<p>One aspect of this that I emphasize is the remarkable parallel between<\/p>\n<ul>\n<li> The usual story of canonical quantization, which is based on an antisymmetric bilinear form on phase space, giving an algebra of operators generated by $Q_j,P_j$ acting on the usual quantum state space.<\/li>\n<li>Replacing antisymmetric by symmetric, you get the Clifford algebra, generated by $\\gamma$-matrices, acting on the spinors.<\/li>\n<\/ul>\n<p>For a table summarizing precisely this parallelism, see chapter 32 of <a href=\"https:\/\/www.math.columbia.edu\/\/~woit\/QMbook\/qmbook-latest.pdf\">the book<\/a>.<\/p>\n<p>For more video from my office, I recently had <a href=\"https:\/\/www.youtube.com\/watch?v=uMn0jUeYf30\">a long conversation with Reza Katebi<\/a>, who has a Youtube channel of interviews called <a href=\"https:\/\/www.youtube.com\/channel\/UCNYrETsy0jDHKhpabjNpXZw\">The Edge of Science<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recently Jean-Pierre Bourguignon recently gave the Inaugural Atiyah Lecture, with the title What is a Spinor? The title was a reference to a 2013 talk by Atiyah at the IHES with the same title. Bourguignon&#8217;s lecture is not yet online, &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12154\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-12154","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12154"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12154\/revisions"}],"predecessor-version":[{"id":12159,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12154\/revisions\/12159"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}