Overblog Suivre ce blog
Editer l'article Administration Créer mon blog

A friendly introduction to the concepts of noncommutative geometry

28 Mai 2013, 15:36pm

Publié par Fabien Besnard

I had the pleasure to talk this friday at this seminar. Now I've just finished cleaning up the notes I had prepared for this talk, and I thought it might be of interest to some of you. Here they are.

 

It is a very low-tech introduction to an introduction, and it should be easy to follow for anybody with undergraduate level in math or physics.

 

Update 11/08/2013 : important remark added at the end of appendix 1.

Commenter cet article

Fabien 09/06/2013 10:30


Thanks cb, for your kind words and your links. I didn't know the second paper, and though I had seen the first, I haven't read it carefully enough to say anything useful about it, unfortunately.
Anyway, I still think some radically new idea is needed in order to make progress on the spectral standard model. Particularly concerning the gravity sector and the incorporation of the Lorentz
signature into the setting.

cb 09/06/2013 00:21


Thank you for these notes, Fabien, you are doing a useful and nice pedagogical work I guess, to promote the
knowledge of the noncommutative geometric "program" for (young) mathematic(ian)s and foster development of its almost-commutative spectral "model" counterpart for (future) high energy
physic(ist)s.


I would like to point readers of your blog to recent progress regarding the last open problem mentioned at the end
of your text, namely the calculation of the Higgs mass. It seems that the last noncommutative model succeeds in postdicting the correct value of the famous Higgs scalar boson recently discovered
at the LHC, providing the existence of another (new) scalar boson much more massive than the Higgs and weakly coupled with it. Even more importantly, this new hypothetical particle happens to be
plausibly responsible for the existence of right Majorana neutrinos and thus also for the very light mass of left ones (http://arxiv.org/abs/1208.1030). Last but not least, the new scalar bosonic field fits nicely
(naturally?) within the noncommutative framework in a possible "grand symmetry” scheme (http://arxiv.org/abs/1304.0415) (http://arxiv.org/abs/1304.8050).


 


Quite interestingly one can add that Alain Connes has already given a nickname to this new scalar
field: the big broson …