tag:blogger.com,1999:blog-6912603287930240451.post1732812072796579189..comments2024-03-29T00:47:51.081+00:00Comments on Noncommutative Geometry: TimeUnknownnoreply@blogger.comBlogger9125tag:blogger.com,1999:blog-6912603287930240451.post-63378276568823250072007-03-31T19:54:00.000+00:002007-03-31T19:54:00.000+00:00I have found a concrete discussion of the relation...I have found a concrete discussion of the relation of the modular operator Delta, that induces the twist sigma that is discussed in the above entry, and the ordinary notion of time evolution of quantum field theory, in the appendix of<BR/><BR/>K.-H. Rehren, On Local Boundary CFT and Non-Local CFT on the Boundary<BR/><BR/>http://golem.ph.utexas.edu/category/2007/03/some_notes_on_local_qft.html#Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-41405358752326345352007-03-26T21:49:00.000+00:002007-03-26T21:49:00.000+00:00Whenever I see infinitely many DoF as in the ac la...Whenever I see infinitely many DoF as in the ac last sentence, “... In QFT the situation is entirely similar and has of course infinitely many degrees of freedom from the start ...“, I have difficulty visualizing infinitely many spatial DoF. <BR/><BR/>Rather, I suspect that such a number of DoF, I suspect that this is more consistent with strategy DoF as successfully used by applied Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-60867029890477707002007-03-26T08:53:00.000+00:002007-03-26T08:53:00.000+00:00Urs: Yes, what happens in fact is that for any qua...Urs: Yes, what happens in fact is that for any quantum system with infinitely many degrees of freedom the hamiltonian H does not belong to the algebra of observables. Thus the corresponding automorphisms are not inner. To see what happens it is simplest to take the case of a system of spins on a lattice. The algebra of observables is the inductive limit of the finite tensor products of matrix AChttps://www.blogger.com/profile/10951419541401211230noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-42626548537373771022007-03-26T07:02:00.000+00:002007-03-26T07:02:00.000+00:00Dear Masoud,many thanks for your reply!I did indee...Dear Masoud,<BR/><BR/>many thanks for your reply!<BR/><BR/>I did indeed have the exponentiated version in mind when I was referring to the "Weyl algebra" obtained from a symplectic manifold. I should have made that more explicit.<BR/><BR/>As far as I understand, the C*-algebra generated from such a Weyl algebra is always all of L(H).<BR/><BR/>Ordinary quantum mechanical time evolution acts on Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-29740725228503725152007-03-23T21:40:00.000+00:002007-03-23T21:40:00.000+00:00Hi Urs and thanks for your comments. Now we ar...Hi Urs and thanks for your comments. Now we are in a higher pitch of course<BR/>(thanks to Alain's recent post!), but I still want to use your earlier<BR/>comments to discuss some elementary aspects of time evolution and a<BR/>non-example! I sense that this may be useful for our larger audience so to speak. As for algebras arising from quantizing symplectic<BR/>manifold, e.g., in the Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-90483829167448627622007-03-22T09:27:00.000+00:002007-03-22T09:27:00.000+00:00Thanks a lot for the explanation for the origin of...Thanks a lot for the explanation for the origin of the outer automorphism. There are fascinating interpretational problems and questions to ponder even with the shaky mathematical background of a physicist. Just one question. Could inner automorphisms be identified as universal local gauge symmetries? In the case of HFFs of type II_1 one can also ask whether outer automorphisms could be seen asMatti Pitkänenhttps://www.blogger.com/profile/13512912323574611883noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-5558654550579846092007-03-21T21:51:00.000+00:002007-03-21T21:51:00.000+00:00Is it posible to relate NCG to the Max Plus Algebr...Is it posible to relate NCG to the Max Plus Algebra of Stephane Gaubert and others [T Basar, GJ Olsder, WM McEneaney]<BR/><BR/>http://www-rocq.inria.fr/MaxplusOrg/<BR/><BR/>http://arxiv.org/abs/math.OC/0609243<BR/><BR/>http://www.math.ucsd.edu/~wmcenean/pubs/Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-87701451577724581402007-03-21T21:22:00.000+00:002007-03-21T21:22:00.000+00:00I'm just a physicist. In our spectral higher opera...I'm just a physicist. In our spectral higher operad approach to mass generation, which is linked to this time emergence, there is no Higgs boson, because the concept of vacuum is unnecessary. Could you see a 'no Higgs boson' SM within your framework?Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-88939017564564543142007-03-21T17:01:00.000+00:002007-03-21T17:01:00.000+00:00Thanks a lot for this detailed reply! I have taken...Thanks a lot for this detailed reply! <BR/>I have taken the liberty of forwarding it to <A HREF="http://golem.ph.utexas.edu/category/2007/03/qft_of_charged_nparticle_the_g.html#c008602" REL="nofollow">this discussion</A>. Hope you don't mind.<BR/><BR/>Can you point me to any literature where the action by outer derivations that you describe is explcitly identified in a concrete field theoretical Anonymousnoreply@blogger.com