tag:blogger.com,1999:blog-73078408250231354842016-09-08T16:32:53.457+12:00Arcadian Pseudofunctoradventures in the brave new world of physicsKeahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comBlogger611125tag:blogger.com,1999:blog-7307840825023135484.post-27822842907796301962012-02-08T11:48:00.000+13:002012-02-08T11:48:00.122+13:00Last PostKea hereby declares Arcadian Pseudofunctor closed.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-92145723364816032832012-02-04T15:18:00.005+13:002012-02-04T15:54:34.371+13:00Conferences ComingAmongst the many interesting, upcoming <a href="http://www.conference-service.com/conferences/high-energy-physics-and-accelerators.html">conferences</a> that I am unable to attend is <a href="http://www.isical.ac.in/~cosgrav12/">Cosgrav 12</a>: International Conference on Modern Perspectives of Cosmology and Gravitation. Oh, look. The <a href="http://www.isical.ac.in/~cosgrav12/#page3">invited speakers</a> all seem to be men, yet again. Perhaps I won't be missing much.<br /><br />Further away, there is <a href="http://moriond.in2p3.fr/">Moriond</a> in March, and a workshop on <a href="http://www.newton.ac.uk/programmes/BSM/bsmw02.html">Scattering Amplitudes</a> at Cambridge in April. <a href="http://research.brown.edu/research/profile.php?id=1154701543">Anastasia Volovich</a> is of course the token woman there, and participation is by invitation only. Meanwhile, the <a href="http://www.ichep2012.com.au/">icHEP12</a> website has a cute disclaimer:<blockquote>In particular, no bona fide scientist will be excluded from participation on the grounds of national origin, nationality, or political considerations unrelated to science.</blockquote>Yes, we need that qualification there, don't we?Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com3tag:blogger.com,1999:blog-7307840825023135484.post-90883603075785687862012-02-03T10:23:00.006+13:002012-02-03T10:31:00.146+13:00Tevatron Strikes BackA <span style="font-weight:bold;">Fairy Update</span>! A new <a href="http://www-cdf.fnal.gov/physics/new/hdg/Results_files/results/hgamgam_dec11/plots.html">CDF analysis</a> of $10$ inverse femtobarns in the $\gamma \gamma$ channel. No fairies.<br /><br /><a href="http://1.bp.blogspot.com/-m_jk5vqH9tg/Tyr-6RqrOdI/AAAAAAAAB9w/ZpuoaXOAHtI/s1600/higgsCDFo.gif"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 290px;" src="http://1.bp.blogspot.com/-m_jk5vqH9tg/Tyr-6RqrOdI/AAAAAAAAB9w/ZpuoaXOAHtI/s400/higgsCDFo.gif" border="0" alt=""id="BLOGGER_PHOTO_ID_5704652155146418642" /></a>Does that $125$ GeV Higgs look a little more uncertain now? Not really, since this is at ten times the SM $\sigma$. Only CMS and ATLAS can tell us the answer.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com0tag:blogger.com,1999:blog-7307840825023135484.post-439761807002824622012-02-01T12:45:00.004+13:002012-02-01T12:52:29.609+13:00Color Z NewsAs discussed a few years ago <a href="http://www.science20.com/quantum_diaries_survivor/new_z_boson_240_gev_no_wait_720">around</a> the physics blogosphere, one possibility for new physics at the LHC was a $720$ GeV state that had <a href="http://kea-monad.blogspot.co.nz/2009/08/fun-at-fermilab.html">something</a> to do with $Z'$ bosons. Evidence for $Z'$ type anomalies, of the non standard kind, has grown in recent years. Now <a href="http://blog.vixra.org/2012/01/31/cms-search-for-exotics-at-5fb/">we hear</a> that the only possible new physics seen by <a href="http://indico.cern.ch/conferenceDisplay.py?confId=174936">CMS</a> is in fact a three event HSCP signal somewhere near $720$ GeV.<br /><br /><a href="http://2.bp.blogspot.com/-VTnSNPN2cPg/Tyh-UihNUXI/AAAAAAAAB9k/mzAQMvOxfIQ/s1600/720newDat.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 296px;" src="http://2.bp.blogspot.com/-VTnSNPN2cPg/Tyh-UihNUXI/AAAAAAAAB9k/mzAQMvOxfIQ/s320/720newDat.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5703947819393306994" /></a>Not much to speak of, three events, but definitely something to ask ATLAS about.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com0tag:blogger.com,1999:blog-7307840825023135484.post-66730874491074273102012-01-31T10:32:00.002+13:002012-01-31T10:35:07.124+13:00Quote of the Month<blockquote>The truth is that sustainable development is fundamentally a question of people’s opportunities to influence their future, claim their rights and voice their concerns. Democratic governance and full respect for human rights are key prerequisites for empowering people to make sustainable choices. The peoples of the world will simply not tolerate continued environmental devastation or the persistent inequality which offends deeply held universal principles of social justice. Citizens will no longer accept governments and corporations breaching their compact with them as custodians of a sustainable future for all.<br /></blockquote>From the new <a href="http://www.un.org/gsp/report">UN report</a>: <span style="font-style:italic;">Resilient People, Resilient Planet: A Future Worth Choosing</span>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com3tag:blogger.com,1999:blog-7307840825023135484.post-53857881743637718152012-01-31T09:00:00.001+13:002012-01-31T09:01:39.216+13:00Quote of the Week<blockquote>I'm vehemently against copyright infringement: the files I lost were created & owned by me for my job.</blockquote>One of 150 million legitimate Megaupload users, whose data has been <a href="http://www.bbc.co.uk/news/technology-16787486">stolen and censored</a> by the US government.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com11tag:blogger.com,1999:blog-7307840825023135484.post-9916886053132402252012-01-27T10:33:00.003+13:002012-01-27T10:34:04.240+13:00Dark MattersRecent dark musings now summarised <a href="http://vixra.org/abs/1201.0097">on vixra</a>.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com5tag:blogger.com,1999:blog-7307840825023135484.post-51250122425252097822012-01-26T10:51:00.000+13:002012-01-26T10:53:51.565+13:00More Than MenFrom the <a href="http://www.morethanmen.org/2012/01/24/on-speakers-and-tokens/">More Than Men</a> project:<blockquote>I can sense the comments coming in already. ”But Sasha,” you ask, “isn’t that just establishing quotas? Aren’t we ignoring qualified dudes because we’re stocking our conferences with woman and minority speakers?” My answer is “No, don’t be so ridiculous and offensive by assuming that trying to create a diverse group of speakers means choosing less-qualified speakers in order to have more than white men talking.<br /><br />Let me say that again, very clearly: If you think that ensuring a diverse representation of genders, races, and physical abilities in your conference speakers means creating a conference stocked with unqualified “tokens” you are making a prejudiced assumption. Your internalized bias is showing. Don’t freak out, it happens to the best of us. So take a deep breath, maybe have a laugh with yourself for freaking out like that and then look a little deeper for those experts who are just too busy doing work and making a name for themselves that you haven’t heard of them yet. Or maybe you have heard of them but didn’t think of them because our brains are lazy and go for the comfortable and familiar rather than stretch a little.</blockquote>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com0tag:blogger.com,1999:blog-7307840825023135484.post-85962470767545795802012-01-22T11:06:00.002+13:002012-01-22T11:07:04.245+13:00Year of the Dragon<a href="http://2.bp.blogspot.com/-Yu5wGDeExm8/Txs25GwIqTI/AAAAAAAAB9Y/UaCTF-dRzsg/s1600/dragonAuckl.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 281px;" src="http://2.bp.blogspot.com/-Yu5wGDeExm8/Txs25GwIqTI/AAAAAAAAB9Y/UaCTF-dRzsg/s400/dragonAuckl.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5700210108060444978" /></a>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1tag:blogger.com,1999:blog-7307840825023135484.post-24230302033067598242012-01-19T09:48:00.002+13:002012-01-19T09:52:23.084+13:00Quote of the Week<blockquote>Don't take our generation lightly</blockquote><a href="http://en.wikipedia.org/wiki/Arfa_Karim">Arfa Karim Randhawa</a> (1995 - 2012)<br />(and at the <a href="http://www.bbc.co.uk/news/world-asia-16599781">BBC</a>)Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1tag:blogger.com,1999:blog-7307840825023135484.post-81915470584061520482012-01-18T14:42:00.008+13:002012-01-18T18:07:00.757+13:00Witten on Yang Mills<a href="http://en.wikipedia.org/wiki/Edward_Witten">Witten</a> speaks at the latest <a href="http://scgp.stonybrook.edu/scientific/workshops/1498">Simons Center</a> conference on <a href="http://www.claymath.org/millennium/Yang-Mills_Theory/">mass gaps</a> in Yang Mills theories. In four dimensions, he stresses that the role of the mass gap is to hide quantum phenomena at large distances, and that no simple perturbation theory can really see the mass gap. A theme of the conference seems to be a renewal of interest in constructive approaches, starting with tractable questions. <br /><br />So the talk focuses on three dimensional theories, starting with the pure Yang Mills action for $R^3$. Here a mass gap exists on dimensional grounds, with $m = w g^2$ for $w$ some constant and $g$ the coupling. But what happens at long distances in three dimensions? Several approaches are briefly reviewed, including (i) a <a href="http://arxiv.org/abs/0906.0783">string tension</a> Hamiltonian approach, and (ii) Feynman and Singer's Hamiltonian for the space $R^2$. In (ii) there is the usual (infinite dimensional) space of connections $A$ and gauge transformations $G$. Witten writes down the basic Hamiltonian<br /><br />$H = g^2 \int \textrm{Tr} E^2 + \frac{1}{g^2} \int \textrm{Tr} B^2$ <br /><br />noting that the first term dominates in the limit $g^2 \rightarrow \infty$, and that the eigenvalues of $H$ should be basic numbers, like $\zeta (2)$. <br /><br />But he appears to believe that a currently <span style="font-style:italic;">tractable</span> approach to mass gaps would look at non-trivial CFTs, for the following reasons. First observe that (in three dimensions) if we add a few essentially massless fermions (like up and down quarks) there is no mass gap. Now we can add a <a href="http://en.wikipedia.org/wiki/Chern%E2%80%93Simons_theory">Chern-Simons</a> term, as a mass gap term, to the usual Yang-Mills action, where $m$ is proportional to $k$, the CS integral coefficient (the fourth dimension is irrelevant). If this (CS) theory is rigorously defined in three dimensions, there should be a theory for any $3$-manifold $M$ with any Riemannian metric. Scale the metric by a factor $t \rightarrow \infty$. That is, we imagine that human experiments are limited by the characteristic scale of the manifold $M$, and at long distances there is the TFT (IR limit). This is of course the context of Jones polynomials and knots.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1tag:blogger.com,1999:blog-7307840825023135484.post-16079064600651826472012-01-18T14:20:00.002+13:002012-01-18T14:25:28.821+13:00The UsualAs expected, the motives <a href="http://vixra.org/abs/1107.0002">paper</a> was summarily rejected by the one referee who looked at it, with some brief comments about my suspicious use of (now) trendy terms. Why this took over six months is beyond me. I also receive about one automated postdoc rejection each day at this time of year (not everyone bothers sending out rejections). I know they are automated, because they usually include a phrase like <span style="font-style:italic;">you and other excellent candidates</span> or <span style="font-style:italic;">we considered your application carefully</span>.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com5tag:blogger.com,1999:blog-7307840825023135484.post-32057393522569075292012-01-18T12:23:00.002+13:002012-01-18T12:24:24.661+13:00Internet FreedomWe support the <a href="http://www.bbc.co.uk/news/technology-16590585">Sopa protest</a>.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1tag:blogger.com,1999:blog-7307840825023135484.post-8547105718153524702012-01-16T17:22:00.005+13:002012-01-16T17:34:48.177+13:00Theory Update 136We can draw the Jacobi rule of knotty <a href="http://pseudomonad.blogspot.com/2011/04/knotty-gauge-theory.html">gauge theory</a> a slightly different way. <br /><br /><a href="http://2.bp.blogspot.com/-cYgA8lzh9YM/TxOmB3Rx3iI/AAAAAAAAB9M/ZnRp7KmHV-c/s1600/aKnotFourT.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 123px;" src="http://2.bp.blogspot.com/-cYgA8lzh9YM/TxOmB3Rx3iI/AAAAAAAAB9M/ZnRp7KmHV-c/s320/aKnotFourT.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5698080504502410786" /></a><a href="http://kea-monad.blogspot.com/2008/05/m-theory-lesson-188.html">Recall</a> the connection to knots in renormalisation <a href="http://kea-monad.blogspot.com/2006/10/connes-kreimer-marcolli.html">theory</a>. The loop formed by the traced braid diagram forms the loop of a chord diagram. The example shown on the right is a <a href="http://kea-monad.blogspot.com/2008/05/m-theory-lesson-189.html">trefoil</a> knot, with zeta value $\zeta (3)$. A <a href="http://vixra.org/abs/1107.0002">double</a> copy of the right hand side of the Jacobi rule appears in the <a href="http://cornellmath.wordpress.com/2007/12/18/chord-diagrams-understanding-the-4t-relation/">4T relation</a>. Now the trivalent vertex on the left of the Jacobi rule is interpreted as a resolution (into trivalent vertices) of the diagram that is half way between the two diagrams on the right (namely the $4$-valent diagram of the node cross over). The pair of Jacobi rules gave us the color kinematic duality of $N = 8$ supergravity.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1tag:blogger.com,1999:blog-7307840825023135484.post-86379726236822103132012-01-15T11:21:00.004+13:002012-01-15T11:35:25.186+13:00Kea At Work<a href="http://4.bp.blogspot.com/-qWrLl2-fILI/TxIAHjKNNdI/AAAAAAAAB9A/DbcoOH01Bg0/s1600/oxfordKea.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 267px;" src="http://4.bp.blogspot.com/-qWrLl2-fILI/TxIAHjKNNdI/AAAAAAAAB9A/DbcoOH01Bg0/s400/oxfordKea.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5697616608274232786" /></a><a href="http://www.ox.ac.uk/media/news_releases_for_journalists/110603.html">far away</a>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com5tag:blogger.com,1999:blog-7307840825023135484.post-68217252323736414032012-01-12T14:19:00.006+13:002012-01-12T14:44:26.301+13:00Theory Update 135A fascinating <a href="http://jcp.aip.org/resource/1/jcpsa6/v135/i15/p151101_s1?bypassSSO=1">new paper</a> by <a href="http://www.princeton.edu/~yjiao/">Yang Jiao</a> and <a href="http://cherrypit.princeton.edu/sal.html">Salvatore Torquato</a> defines three dimensional packings of <a href="http://kea-monad.blogspot.com/2008/07/carbon-beauty-iv.html">truncated</a> tetrahedra, using a lattice vector deformation parameter $g$ that takes values in the interval $[0,2/9]$. <br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/-jhoyWEmzCrk/Tw41O0jLE1I/AAAAAAAAB80/ri99-B5OU60/s1600/aTetPack4.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 182px;" src="http://3.bp.blogspot.com/-jhoyWEmzCrk/Tw41O0jLE1I/AAAAAAAAB80/ri99-B5OU60/s400/aTetPack4.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5696549107410867026" /></a>A trucated tetrahedron has four hexagonal faces and four triangular ones. The maximal $g = 2/9$ corresponds to the densest known packing of truncated tetrahedra, with packing fraction $207/208$. The packing has tetrahedra shaped holes. With Conway they have also <a href="http://www.pnas.org/content/103/28/10612">constructed</a> a packing with fraction $23/24$, and considered packings involving <a href="http://www.pnas.org/content/108/27/11009">octahedra</a>.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com4tag:blogger.com,1999:blog-7307840825023135484.post-20815419088373271372012-01-11T15:01:00.007+13:002012-01-11T15:37:55.295+13:00Theory Update 134In the <a href="http://www.as.huji.ac.il/schools/phys29/recorded_lectures">new lectures</a>, Arkani-Hamed reviews basic twistor geometry. As usual we work with the $N = 4$ theory, because that is the amount of supersymmetry in the complex numbers $C$. The <a href="http://arxiv.org/abs/1102.1193">bioctonion</a> case of $C \cdot C$ allows us to <a href="http://vixra.org/abs/1107.0002">discuss</a> $N = 8$ supergravity. In the lectures, traditional supersymmetry is used to obscure the categorical structure of the combinatorics. Recall that a trivalent vertex may be used to represent a point associahedron, and comes in two allowed helicity triplets. <br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/-eGtoOMwmABA/TwztmweqIpI/AAAAAAAAB8o/XfEw3t-Vm-g/s1600/aSourceTriv.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 214px; height: 140px;" src="http://4.bp.blogspot.com/-eGtoOMwmABA/TwztmweqIpI/AAAAAAAAB8o/XfEw3t-Vm-g/s320/aSourceTriv.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5696188878821139090" /></a>The counting of $\textrm{N}^{k}\textrm{MHV}$ terms for $n$ legs is given by the <a href="http://en.wikipedia.org/wiki/Catalan_number">Catalan</a> number of the appropriate <a href="http://pseudomonad.blogspot.com/2011/04/theory-update-77.html">associahedron</a>. The distinct trivalent vertices may then define a directed associahedron edge, via their representation as <span style="font-style:italic;">points</span>. <br /><br />Arkani-Hamed stresses the importance of Grothendieck's mathematics and other motivic mathematics, such as the <a href="http://kea-monad.blogspot.com/2006/10/connes-kreimer-marcolli.htmlConnes-Kreimer">Connes-Kreimer</a> approach to renormalisation. However, there still appears to be a belief that this will all work out without any abstract airy fairy category theory. Although he admits a previous long term allergy to all things motivic, there is obvious excitement about the new connections to the interests of mathematicians like Deligne. Unofficially, the lectures are about the <span style="font-style:italic;">positive Grassmannian</span> (which is, of course, all about generalised <a href="http://arxiv.org/abs/math/0312297">associahedra</a>).Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com3tag:blogger.com,1999:blog-7307840825023135484.post-81659973754816000472012-01-11T13:51:00.002+13:002012-01-11T13:55:10.911+13:00News from FermiFrom <a href="http://www.nasa.gov/mission_pages/GLAST/news/energy-extremes.html">Fermi LAT</a>:<blockquote>One example is the well-known radio galaxy <a href="http://en.wikipedia.org/wiki/NGC_1275">NGC 1275</a>, which is a bright, isolated source below 10 GeV. At higher energies it fades appreciably and another nearby source begins to appear. Above 100 GeV, NGC 1275 becomes undetectable by Fermi, while the new source, the radio galaxy <a href="http://arxiv.org/abs/1003.4615">IC 310</a>, shines brightly.</blockquote>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com0tag:blogger.com,1999:blog-7307840825023135484.post-92072212293602858172012-01-10T08:52:00.002+13:002012-01-10T08:57:23.854+13:00Quote of the MonthFrom <a href="http://www.math.columbia.edu/~woit/wordpress/?p=4364">Woity Toity</a>:<blockquote>As usual, <a href="http://www.ias.edu/people/faculty-and-emeriti/arkani-hamed/">Arkani-Hamed</a> makes wildly enthusiastic claims. In this case, he claims to have finally found a remarkable new understanding of the subject, based on some <a href="http://kea-monad.blogspot.com/2006/09/more-on-batanins-operads.html">combinatorial</a> objects and dramatic new mathematical ideas. He does note that this still hasn’t been written up, and that it’s the third time in the past year that he has thought he had things understood, with the last two times not working out.</blockquote>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com7tag:blogger.com,1999:blog-7307840825023135484.post-41600633283880872632012-01-09T16:16:00.002+13:002012-01-09T16:21:58.266+13:00Women A MysteryIt seems the biggest news of the day, around the <a href="http://cosmiclog.msnbc.msn.com/_news/2012/01/05/9981931-what-mystifies-dr-hawking-women">blogs</a> and in <a href="http://www.guardian.co.uk/science/2012/jan/04/stephen-hawking-women-complete-mystery">the press</a>, is that <a href="http://en.wikipedia.org/wiki/Stephen_Hawking">Hawking</a> said women were a complete mystery, which is not surprising for someone who never actually had to work with any women. So I scoured the bemused stories, looking for any mention of sexism or feminism, with regard to any of the parties involved, but of course to no avail. Perhaps there is one somewhere. Only in the comments sections did I find some relief. <a href="http://www.aol.com/social/Melodie_Benford/stephen-hawking-women-a-mystery_n_1184468_127105777.html">Melodie Benford</a> summed it all up: <blockquote>I find this article so freakin sexist ...</blockquote>Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1tag:blogger.com,1999:blog-7307840825023135484.post-64524839865278102672012-01-09T12:29:00.002+13:002012-01-09T12:39:57.032+13:00More Quick NeutrinosI was told that <a href="http://www.newscientist.com/">New Scientist</a> had yet <a href="http://www.newscientist.com/article/dn21328-fasterthanlight-neutrinos-dealt-another-blow.html">another story</a> on the impossibility of superluminal neutrinos, but it turns out to be yet another case of imposing a classical concept of energy on a phenomenomen that quite clearly won't be adequately explained by such a theory, if true. Weak logic makes poor news. Back in OPERA <a href="http://pseudomonad.blogspot.com/2011_09_01_archive.html">month</a>, we mentioned classical <a href="http://en.wikipedia.org/wiki/Tachyon">tachyons</a>, whose low energy states move at the <span style="font-style:italic;">fastest</span> speed, but this old rule could easily be inverted in quantum gravity, so that tachyons travelling <a href="http://pseudomonad.blogspot.com/2011/09/rumour-no-more.html">just faster</a> than $c$ are the <a href="http://www.newscientist.com/article/dn21328-fasterthanlight-neutrinos-dealt-another-blow.html">black sheep</a>. <br /><br />A more interesting article from this edition is a note on <a href="http://www.newscientist.com/article/mg21328465.800-mundane-dark-matter-may-lurk-in-starry-clusters.html">dark matter</a> in globular clusters.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com0tag:blogger.com,1999:blog-7307840825023135484.post-89109682481403411132012-01-05T16:44:00.003+13:002012-01-05T16:49:29.564+13:00Quick Neutrino ReviewSome <a href="http://kea-monad.blogspot.com/2008/06/m-theory-lesson-197.html">years ago</a> we were wondering about the relation between <a href="http://kea-monad.blogspot.com/2010/04/m-theory-lesson-309.html">neutrino</a> physics and the <a href="http://en.wikipedia.org/wiki/McKay_correspondence">McKay</a> correspondence, for the exceptional groups $E_6$, $E_7$ <a href="http://kea-monad.blogspot.com/2007/02/regular-irregular-ii.html">and</a> $E_8$. Much has happened since then, in the twistor world, in the Jordan algebra world, and in the cat world. It is clear that exceptional structures play an important role in gravity.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com2tag:blogger.com,1999:blog-7307840825023135484.post-84430178379451617672012-01-05T15:27:00.013+13:002012-01-05T15:49:40.264+13:00Dark Matter UpdateLet us <a href="http://pseudomonad.blogspot.com/2011/10/dark-matter-at-lhc.html">recall</a> the basic <a href="http://pseudomonad.blogspot.com/2011/10/dark-matter-at-lhc-ii.html">dark matter</a> fractions in the quark gluon plasma. That's $3 / 4 \pi$ for the dark matter fraction and $9/ 4 \pi$ for the (so called) dark energy, with the baryonic fraction $\Omega_{b} = 1 - 3/ \pi$, as <a href="http://riofriospacetime.blogspot.com/2010/12/wmap.html">confirmed</a> by WMAP.<br /><br />In the information theory, we need two kinds of <span style="font-style:italic;">dimension</span>. First, path bases define an integral dimension, $27$ for the <a href="http://math.ucr.edu/home/baez/octonions/node12.html">Jordan</a> algebra. But complex matrix entries tend to be characters for finite fields, so that the root of unity corresponding to a phase $2 \pi /27$ would specify the cardinality of a field with $27$ elements. These two dimension types should be related by the mirror physics that explains the dark matter fractions. <br /><br />A dark matter ansatz: the total dark sector density fraction $\Omega_{d}$, as a fraction of the <span style="font-style:italic;">character</span> dimension for $27$ paths, equals the observable universal fraction of the <span style="font-style:italic;">integral</span> dimension. In other words, we would like to write<br /><br />$ \frac{3}{\pi} \frac{2 \pi}{27} = \frac{2}{9} $<br /><br />so that $\Omega_{d} = 3/ \pi$. Now observe that we can split the dark sector into quark and lepton components. The leptonic dark matter fraction $3/ 4 \pi$ now corresponds to the fraction $1/18$, a single quark path from the quark set. Similarly, the dark energy fraction $9/ 4 \pi$ corresponds to the fraction $1/6$, a single lepton path. The total $3/ \pi$ is then the only solution obeying this quark lepton complementarity. <br /><br />In the quark gluon <a href="http://pseudomonad.blogspot.com/2011/10/dark-matter-at-lhc.html">plasma</a>, the minimal viscosity to entropy ratio is $1/ 4 \pi$. As a character dimension fraction, $1/ 4 \pi$ corresponds to $1/54$, a single basis path in the full bioctonion <a href="http://arxiv.org/abs/1005.3514">algebra</a>.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com8tag:blogger.com,1999:blog-7307840825023135484.post-7064443995263398652012-01-03T12:51:00.004+13:002012-01-03T13:29:40.121+13:00Auld Lang SyneAs <a href="http://books.google.co.nz/books?id=Sqp0aa4f72EC&pg=PA272&lpg=PA272&dq=knot++%22quantum+code%22&source=bl&ots=r4vmkwKBw5&sig=rqKhy6EtN4Q6l42zsHIjSgavKUM&hl=en&sa=X&ei=L0ICT_qcIoKViQeI7KzhBg&ved=0CBwQ6AEwAA#v=onepage&q=knot%20%20%22quantum%20code%22&f=false">Kitaev</a> will tell you, <span style="font-style:italic;">quantum codes</span> are about things like <a href="http://en.wikipedia.org/wiki/Braided_monoidal_category#Ribbon_categories">ribbon categories</a>. Ribbons and knots, knots and ribbons. <br /><br />Back in the mid '90s, everyone was <a href="http://pseudomonad.blogspot.com/2011/12/through-looking-glass-iii.html">into</a> quantum field theories with knots. I was supposed to be working in standard lattice QCD, in a Physics department, but being enamoured of knots I instead found myself lost amongst the deserted stacks of the mathematics library, and chatting to mathematicians like <a href="http://maths.anu.edu.au/~wangb/">Bai-Ling Wang</a> and <a href="http://maths.anu.edu.au/~acarey/">Alan Carey</a>. At that time, classical <a href="http://en.wikipedia.org/wiki/Contact_manifold#Legendrian_submanifolds_and_knots">geometry</a> was still boss, and everywhere I looked there were manifolds, manifolds, manifolds. The mathematicians weren't at all bothered by all the manifolds, but as a physicist who haunted the library stacks, I was looking for something more, let's say, <span style="font-style:italic;">background independent</span>. Alan gave me some excellent advice, and told me to work on my thesis and forget about the knots (but naturally, the advice was bound to be ignored). <br /><br />Anyway, a standard gadget in the knotty manifold world was a <a href="http://en.wikipedia.org/wiki/Framed_knot">framed knot</a>, where one thickened a knot into a kind of twisted torus so that it sat in a <a href="http://arxiv.org/abs/math/0412330">nice way</a> in a larger space. By drawing lines along the torus, one could get ribbon diagrams. For example, quantum mathematicians liked symplectic spaces, such as $T^{*}S^3$, the <a href="http://en.wikipedia.org/wiki/Cotangent_bundle#The_cotangent_bundle_as_phase_space">cotangent bundle</a> of the three dimensional sphere $S^3$. Such a six dimensional space has three dimensional <a href="http://en.wikipedia.org/wiki/Symplectic_manifold#Lagrangian_and_other_submanifolds">Lagrangian</a> submanifolds, good for putting knots in, and with which mathematicians can <a href="http://arxiv.org/abs/math/0412330">do some</a> knot wizardry. <br /><br />In time, the trend moved towards <a href="http://arxiv.org/abs/1109.1542">combinatorial</a> alternatives. The only constant was the <a href="http://en.wikipedia.org/wiki/Category_theory">universal</a> obsession with knots and ribbons. Six strands <a href="http://pseudomonad.blogspot.com/2011/03/theory-update-75.html">for</a> three ribbons. I could no longer afford to listen to mathematics lectures in Princeton or Canberra, and nobody was willing to supervise my thesis proposal on a lovely $7$ dimensional Chern-Simons theory, so I went to Wanaka and bumped chairs and served chips to hungry skiers, and worried instead about the bottletops that my flatmate insisted on leaving all over the floor.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com3tag:blogger.com,1999:blog-7307840825023135484.post-86461620752883636282012-01-01T14:41:00.006+13:002012-01-01T15:05:32.371+13:00Higgsy Codes IVThe cubed root symbol $\omega$ may be thought of as a non zero element in the four element <a href="http://en.wikipedia.org/wiki/Finite_field">field</a>. In the <a href="http://en.wikipedia.org/wiki/Hexacode">hexacode</a> description of the <a href="http://en.wikipedia.org/wiki/Miracle_Octad_Generator">miracle octad</a> there are $3 \times 6$ arrays, that is, three length $6$ words in four letters. A key three word matrix is built from the $3 \times 3$ identity and the Fourier operator, <br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/-0rZACrUH7j8/Tv-55n_hJuI/AAAAAAAAB8c/t95C9qSIEKw/s1600/bMatHexcod.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 246px; height: 115px;" src="http://1.bp.blogspot.com/-0rZACrUH7j8/Tv-55n_hJuI/AAAAAAAAB8c/t95C9qSIEKw/s320/bMatHexcod.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5692472853658674914" /></a>in analogy to the (gauge fixed) $2 \times 4$ arrays that create a Grassmannian Minkowski space in the $2 \times 2$ twistor formalism. <a href="http://en.wikipedia.org/wiki/John_Horton_Conway">Conway</a> has a similar construction for the <a href="http://en.wikipedia.org/wiki/Ternary_Golay_code">ternary code</a>, known as <a href="http://books.google.co.nz/books?id=upYwZ6cQumoC&pg=PA299&lpg=PA299&dq=miniMOG+++conway+ternary&source=bl&ots=_LZU_YddzU&sig=84RRw-_QoanUkf95TY3ksQeQs74&hl=en&sa=X&ei=Tbz_Tt-iO660iQeqpYy4AQ&ved=0CCQQ6AEwAQ#v=onepage&q=miniMOG%20%20%20conway%20ternary&f=false">miniMOG</a>. The hexacode is used to specify five points from which a Steiner octad is created.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com1