tag:blogger.com,1999:blog-8883034.post7499178151676606817..comments2024-01-27T12:50:11.862+01:00Comments on atdotde: Questions to the inter webs: classical 't-Hooft-limit and path integral entanglementRoberthttp://www.blogger.com/profile/06634377111195468947noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-8883034.post-59395965760989120742014-04-15T13:33:42.632+02:002014-04-15T13:33:42.632+02:00"The 't Hooft limit leads to important si..."The 't Hooft limit leads to important simplifications in perturbative QFT ..." Does 't Hooft determinism lead to even more important simplifications?<br />"We claim that our observations add a new twist to discussions concerning the interpretation of quantum mechanics, which we call the cellular automaton (CA) interpretation.” — G. 't Hooft<br /><a href="http://arxiv.org/abs/1207.3612" rel="nofollow">"Discreteness and Determinism in Superstrings", 2012 by Gerard 't Hooft</a><br /><a href="http://vixra.org/abs/1203.0036" rel="nofollow">Does the Fernández-Rañada-Milgrom Effect Explain the Flyby Anomaly?</a>David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-50463448846459623782014-02-04T14:01:30.934+01:002014-02-04T14:01:30.934+01:00Actually you can think of planar Yang-Mills in exa...Actually you can think of planar Yang-Mills in exactly the way you described above, i.e. at infinite N the path integral is exactly determined by a single saddle point, which is given by a set of 4 infinity by infinity matrices, which are usually dubbed master field, however as far as I can tell nobody has so far managed to make any use of that or determine any properties of these.<br />The original source for this are some old lecture notes by Witten called "The 1 / N Expansion In Atomic And Particle Physics" , which you can find here:<br />http://www-lib.kek.jp/cgi-bin/img_index?8002242<br /><br />Is this what you were looking for?Alexanderhttps://www.blogger.com/profile/07235510573788847842noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-77536191307381817382014-02-03T13:21:47.869+01:002014-02-03T13:21:47.869+01:00I finally got hold of the Floratos etal paper. Th...I finally got hold of the Floratos etal paper. They build on Jens Hoppe's way of viewing area preserving diffeos of a membrane (they write S^2 but in fact any two dimensional surface will do) as some N->infinity limit of SU(N). They argue that that this allows them to interpret the gauge indices as fourier decomposition of two additional coordinates. I don't see that this would in any way be related to planarity of feynman diagrams.Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-2335192720349748402014-01-30T17:04:42.803+01:002014-01-30T17:04:42.803+01:00You can compute correlation functions in the path ...You can compute correlation functions in the path integral formalism. There you do have a notion of locality. So you could characterize entanglement by studying how these correlation functions behave. And you do have a notion of non-classical behavior, since you can compute these correlation functions with the ``classical'' measure or by taking the corrections into account-perturbatively (e.g. loop expansion) or non-perturbatively (e.g. lattice regularization).Anonymoushttps://www.blogger.com/profile/06379940898372024773noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-38939705189146581022014-01-30T16:42:20.799+01:002014-01-30T16:42:20.799+01:00Of course they don't factorise but that you al...Of course they don't factorise but that you already have for correlations (which can be classical). I am asking about entanglement which manifests itself in violations of inequalities that are obeyed classically.Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-68898293981281786192014-01-30T14:45:53.831+01:002014-01-30T14:45:53.831+01:00Two interacting particles 1,2 are in general entan...Two interacting particles 1,2 are in general entangled - you see this in the path integral Z as the fact that it does not factorize as Z1*Z2.<br />But I guess I am missing the point of your question...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-38228195388444995642014-01-29T21:29:15.383+01:002014-01-29T21:29:15.383+01:00Regarding the first topic:
1/N plays the role of...Regarding the first topic: <br /><br />1/N plays the role of ``Planck's constant'', i.e. it's the quantization parameter. So the limit N->oo is the semi-classical limit.<br /><br />Maybe this <br /><br />E. G. Floratos, J. Iliopoulos and G. Tiktopoulos,<br /> ``A NOTE ON SU(infinity) CLASSICAL YANG-MILLS THEORY,''<br /> Phys. Lett. B217 (1989) 285<br /><br />would be relevant?Anonymoushttps://www.blogger.com/profile/06379940898372024773noreply@blogger.com