tag:blogger.com,1999:blog-6912603287930240451.post2315459915443996546..comments2023-08-16T08:02:29.630+00:00Comments on Noncommutative Geometry: Noncommutative spacetimeUnknownnoreply@blogger.comBlogger14125tag:blogger.com,1999:blog-6912603287930240451.post-56082003818111361292008-08-01T11:38:00.000+00:002008-08-01T11:38:00.000+00:00Hello,I see that in the fourth comment above Alain...Hello,<BR/><BR/>I see that in the fourth comment above Alain Connes said that<BR/><BR/>"My intention is to use this blog, this summer holidays, to explain [the] content [of articles on the NCG standard model] in details".<BR/><BR/>Maybe these discussions haven't appeared on the blog so far, or did I miss them? (just asking)<BR/><BR/><BR/>Over at the n-category Café I am having a Unknownhttps://www.blogger.com/profile/01006460812296046328noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-36091728276024960592008-03-19T16:32:00.000+00:002008-03-19T16:32:00.000+00:00Dear Alain,you alluded in your text to Thurston's ...Dear Alain,<BR/>you alluded in your text to Thurston's theorem about the simplicity of the identity component of diffeo groups. As far as I know, this works for closed manifolds. With a noncompact Lorentzian manifold M as a base space, I guess one could still imagine to cook up a bundle X over M such that diff(X) is the semi-direct product of diff(M) with the SM gauge group G. Or is there a way Fabien Besnardhttps://www.blogger.com/profile/00975996576182366143noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-11167123267859774932007-09-18T12:47:00.000+00:002007-09-18T12:47:00.000+00:00About the finite space of the Standard Model, and ...About the finite space of the Standard Model, and while we wait to hear more from it in this blog, I have been reading a bit more on the history of extra dimensional spaces of string theory. Gliozzi-Scherk-Olive, in 1977 "Supersymmetry, Supergravity theories and the dual spinor model" stress their need of Majorana-Weil spinors and then "<I>The requeriment ... gives thus the following condition onAlejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-27262537282781722462007-07-08T11:35:00.000+00:002007-07-08T11:35:00.000+00:00I believe that the extension of the "symplectic" f...I believe that the extension of the "symplectic" framework to the NC world is simply the notion of the first order term in a deformation of the NC-algebra. This is quite clear in the commutative case where a symplectic structure (or more generally Poisson structure) is just the first term in the expansion of the deformed product. Thus it is a semi-classical form of the deformation. In the NC AChttps://www.blogger.com/profile/10951419541401211230noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-46226274865232812202007-07-08T02:21:00.000+00:002007-07-08T02:21:00.000+00:00Dear anonymous and Hyun Seok. Here is what I think...Dear anonymous and Hyun Seok. Here is what I think about your question and answer. In Connes' notion of `spectral triple' we have a remarkable extension of the idea of spin Riemannian manifolds to a noncommutative setting. It is based on a non-trivial spectral realization of the distance in Riemannian geometry using the Dirac operator. The definition of a NC symplectic manifold, whatever itAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-7732332798605121262007-07-07T18:55:00.000+00:002007-07-07T18:55:00.000+00:00Dear kea,unfortunately, this picture has not been ...Dear kea,<BR/><BR/>unfortunately, this picture has not been condensed yet into a compact form although it is ubiquitous in recent string theory papers. But you may consult the following papers: arXiv:0704.0929 [hep-th]; hep-th/0612231; hep-th/0611174. Sorry, they are mine -.-.Unknownhttps://www.blogger.com/profile/00823936427601130158noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-35130965151064204242007-07-07T15:33:00.000+00:002007-07-07T15:33:00.000+00:00Dear anonymous,A famous example of NC phase space ...Dear anonymous,<BR/><BR/>A famous example of NC phase space is quantum mechanics. Quantum mechanics is by definition the formulation of mechanics in "NC phase space". So a paricle phase space in quantum mechanics is an example of NC symplectic manifold.Unknownhttps://www.blogger.com/profile/00823936427601130158noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-5583009286999764232007-07-06T17:03:00.000+00:002007-07-06T17:03:00.000+00:00This is a question for Hyun Seok. In your comment ...This is a question for Hyun Seok. In your comment you mention NC `phase space. ' Do you know any precise definition of a NC phase space, e.g. a NC symplectic manifold? Can anyone comment on this?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-61342974060382251522007-07-05T21:46:00.000+00:002007-07-05T21:46:00.000+00:00Hyun SeokYour comment on the equivalence principle...Hyun Seok<BR/><BR/>Your comment on the equivalence principle is very interesting. Could you possibly provide us with references?Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-22022484647149577602007-07-05T11:53:00.000+00:002007-07-05T11:53:00.000+00:00Dear Alain,thank you for your inspiring post.Let m...Dear Alain,<BR/><BR/>thank you for your inspiring post.<BR/>Let me briefly outline a recent understanding about gravity based on noncommutative geometry. <BR/>Recent developments from string theory imply that gravity may be emergent from gauge theories in noncommutative spacetime or large N gauge theories like as the AdS/CFT duality.<BR/>As your motto, geometry is emergent from (noncommutative) Unknownhttps://www.blogger.com/profile/00823936427601130158noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-9861614743420543292007-07-04T19:10:00.000+00:002007-07-04T19:10:00.000+00:00Dear FabienYour question is pertinent. The role of...Dear Fabien<BR/><BR/>Your question is pertinent. The role of the finite space is now much better understood from the very recent papers with A. Chamseddine: "why the Standard Model" and "A dress for SM the beggar" which are on the hep-th arXiv. My intention is to use this blog, this summer holidays, to explain their content in details, but one step at a time. So far I just wanted to explain why AChttps://www.blogger.com/profile/10951419541401211230noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-10095293479596008522007-07-04T18:59:00.000+00:002007-07-04T18:59:00.000+00:00Guy on the street, just try to permute some letter...Guy on the street, just try to permute some letters and get 4 times a name which is not so difficult to guess.......what can you come up with starting with "non alsacien" for instance?AChttps://www.blogger.com/profile/10951419541401211230noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-6359085703615978242007-07-04T16:40:00.000+00:002007-07-04T16:40:00.000+00:00Dear Alain, thank you for this post.I'm going to a...Dear Alain, thank you for this post.<BR/>I'm going to ask a question which is probably terribly naive and possibly a bit crazy. As I understand, classical Kaluza-Klein theory suffers form the drawback of instability of the extra compact dimensions which would tend to shrink down to singularities. Now, correct me if i'm wrong, but the finite NC part A_F of the algebra C(M)\tensor A_F can be seen Fabien Besnardhttps://www.blogger.com/profile/00975996576182366143noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-71036395490728136002007-07-04T16:12:00.000+00:002007-07-04T16:12:00.000+00:00Well... I want to know what the riddle means! Any...Well... I want to know what the riddle means! Any hints as to where commutativity should be applied?Anonymousnoreply@blogger.com