{"id":12099,"date":"2021-04-01T12:25:48","date_gmt":"2021-04-01T16:25:48","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12099"},"modified":"2021-04-02T14:29:11","modified_gmt":"2021-04-02T18:29:11","slug":"twistor-unification","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12099","title":{"rendered":"Twistor Unification"},"content":{"rendered":"

I’ve finally finished writing up a new version of some ideas that I first wrote about here last summer<\/a>. The latest draft is here<\/a>, I may set up a web page with more info here<\/a>.<\/p>\n

Several people had very helpful comments on what I wrote last summer, especially in pointing out that I wasn’t providing sufficient justification for the most radical claim I was making, that the problems with analytic continuation of spinor fields indicated that one could interpret one of the Euclidean space rotation group SU(2)s as an internal symmetry. I then spent a lot of time mastering aspects of Euclidean QFT I had never properly understood. Section two of the current paper is the result. It’s in some sense quite elementary, people may find it of independent interest, even if you’re not interested in the ideas involving twistors. Section three, an exposition of relevant aspects of twistors, is pretty much unchanged. Section 4 is an outline of the ideas about how to get a unified theory out of twistors, much there is still sketchy. I understand a lot better than last year how what I’m proposing fits into some standard ideas about “chiral” formulations of gravity, also have learned a bit more about previous attempts to formulate chiral gravity and gauge theory on twistor space. Some highly speculative remarks that this might all be somewhat related to N=4 super Yang-Mills have been added.<\/p>\n

Here’s a little bit more here about the hardest to believe claim being made (about analytically continuing spinors). The standard assumption (this is what I always thought) has been based on the analytic continuation behavior of correlation functions: Schwinger and Wightman functions are analytic continuations of each other, and one might think there’s nothing more to analytic continuation between Euclidean and Minkowski space theories. After learning more about the Euclidean QFT literature, I was struck by how different this is from the physical Minkowski space formalism: states and fields don’t just analytically continue, they’re quite different sorts of objects in the Euclidean case. Anyway, this is all explained in detail in the paper…<\/p>\n

Update<\/strong>: No, this is not an April Fool’s joke. I’ve now created a twistor unification page<\/a> where I’ll try and maintain updated information about this unification proposal<\/p>\n","protected":false},"excerpt":{"rendered":"

I’ve finally finished writing up a new version of some ideas that I first wrote about here last summer. The latest draft is here, I may set up a web page with more info here. Several people had very helpful … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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":"","jetpack_post_was_ever_published":false},"categories":[31],"tags":[],"class_list":["post-12099","post","type-post","status-publish","format-standard","hentry","category-twistor-unification"],"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\/12099","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=12099"}],"version-history":[{"count":7,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12099\/revisions"}],"predecessor-version":[{"id":12268,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12099\/revisions\/12268"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}