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1. Robert McNees (mcnees@mastodon.social)'s status on Thursday, 21-Dec-2023 14:34:36 UTC Robert McNees

   in reply to

   • John Carlos Baez
   • Garrett Lisi

   @johncarlosbaez @Garrett I remember Marcus meeting with her and asking for something to work on. She just pulled that topic from the famous “problem drawer” in her file cabinet, and told him to get to work.

   https://mastodon.social/@mcnees/109552520631559327

   • John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:34:38 UTC John Carlos Baez

     in reply to

     • Garrett Lisi

     @Garrett - you may be interested in Cecile DeWitt-Morette's article on CPT and the physical difference between Pin(1,3) and Pin(3,1):

     https://arxiv.org/abs/math-ph/0012006

     Teaser:

     "In a neutrinoless double beta decay, the neutrino emitted and reabsorbed in the course
     of the interaction can only be described in terms of Pin(3,1)"

     not Pin(1,3).

     You can skip Section 0 until it matters.

     (2/2)

   • John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:34:42 UTC John Carlos Baez

     in reply to

     • Garrett Lisi

     @Garrett - that's really interesting! I'll have to think abot whether these 8 double covers are related to the 8 in the 10-fold = 8+2-fold way. That is, whether these 8 covers are at all related to the 8 Morita equivalence classes of real Clifford algebras. It's sure not obvious, but it's tempting!

     It's VERY weird that (some?) quantum field theorists are using a cover that's neither Pin(1,3) nor Pin(3,1), since pinors work for those pin groups.

     (1/2)

   • Garrett Lisi (garrett@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:35:03 UTC Garrett Lisi

     in reply to

     • John Carlos Baez

     @johncarlosbaez Apparently quantum field theorists have chosen to live in (-,-,-), which is neat because then P and T can be associated with quaternions, but weird because I don't think it corresponds to either Pin(1,3) or Pin(3,1), but rather to one of the other Pin groups double covering O(1,3). This stuff is pretty fascinating, and getting me more interested in finite groups.

     (2 of 2)

   • John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:35:13 UTC John Carlos Baez

     in reply to

     • Garrett Lisi

     @Garrett - P and T commute in many situations, e.g. in a scalar field theory. I don't know why they'd anticommute...

   • Garrett Lisi (garrett@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:35:21 UTC Garrett Lisi

     • John Carlos Baez

     @johncarlosbaez Is it worth mentioning that C and T commute? (Or maybe there are weird cases where they don't?) And, if I understand things right, in particle physics C and P also commute but P and T anticommute?