Tuesday, March 18, 2008

Status of the blog

I have writen relatively few (here and in forums) in the las times. This doesn´t mean that I would have somewhatleft the physici, quite on the contrary.

Cronologicaly the first reason to stop me writng was to do a sistematic reading of Jackes Distler´s blog. That gave me a partial idea of what had been hapening in string theory and quantum gravity in general in the very last years. One of the things that one can learn there are that some of the discusions betwen the LQG comunity and the string comunity come from online discusions. Particularly it was interesting, concerning this "string wars" a post with around 100 answers about chirality in LQG. AS a consecuence of that reading I studied the chapter on chirality of he book "topology and quantum field theory" together with all the preliminars required for it (Sheave comology, some basic K theory and Atiyha singer theorem explianed in that framework, certinly not trivial things). I had readed some chapters of that book previously, but I practically had to reread them, together with some ampliations to get (aprt of the above mentioned) a, still far for finished, understanding of anlgebraic geometry. In fact that chapter, in my opinion, is far for complete, and maybe I will read in the future some of the available reviews. Anyway I think I got a decent idea of the arguments of Distler against the Smollin arguments. In fact i guess that a better defense could have been made of the case for LQG. As I understand the problem the reason why you can´t have chiral matter in LQG is that LQG is thinked by string people as some kind of latice theory. But in latice theries you can´t have chiral matter because of the period doulbing problem (there are many places to study an introduction to QFT on the latice. Perhaps my favourite one is the chapter of the Michio Kaku book on QFT). But the thing is that, as far as I undertand it the way the spin network is thinked (or wishefull thinked, who knows?)in LQG isn´t exactly a latice theory. In particular there is no topology in spin networks, or spinfoams for what matters, (LQG is a pre-topology theory)and It would evade the topological character whch make chirality a deep nature beyond their perturbative appearence in the famous triangle Feynman graph. But, certainly, if the LQG cmunity didn´t did that defense it probably means that I am loosing some point, that is, they are the experts, I have a reasonable knowledge of canonical LQG and, to a lesser extent, sin foams, but for sure I am not an expert.

Another thing that I learned, about the string wars, in Distler´s blog is that prt of it happened in the, sadly stopped, string coffee blog. I have the intention of reading it sistemathicallly also, but some things prevented me form doing it. For example reading comments about the Lisi´s E(8) theory I realized that what I had been teached about group theory in the course at the university was far from enought. I still think, as I expresed before that group theory aalone isn´t going to give answers to quntum gravity problems. But anyway It was obvious that I needed to learn better the subject. It was a very, very ugly task. As I have said in this blog my mathemathical formation is s mathemathician, rather than as phyisician, so for me the books of group theory for phyisic are somewht like a nightmare. In mathemathics a Lie group is a relatively easy thing to understand once you understand geomtery in manifolds. The definitions are elegant and natural. In physics the idea of continous groups, in the sense of calculus, and matrix groups seems rogught, and maybe even limited. But if at the level of the group the discrepances are relatively solvables at the level of the Lie algebra the problems row fast and it is almost an act of faith to belive that definitions ocf Cartan subalgebras, root vectors and almost everything are the same as stated in, for example, the book of Georgy (Lie algebras in particle physics) and in, for example, the book of Sattinger and Weaver (symmetry groups, geometry and physics, if I don´t remmeber bad the title) where they are introduced using notions of abstract álgebra (solvable ideals and thngs like that). An added problem is that mathemathicians interest in Lie groups seems to be the clasification of symmetric spaces more than in particle physic (although they also cover it, mainly the "wight fold way). Well, anyway I, at last, learned properly about the relation betwen ral and complex forms of a lie aalgebra and it´s consequences. One added problem with group theory, as teached by mathemathicians, is that they make a good cover of the clasification of Lie algebras, and give a quick tour in representation theory (including sinor representations of some algebras). But htey uses very, relatively, asic techniches. A physicans book, on the contrary, gives an in deep tratement on SU(n) wiht basic, as well as tensor methods and the younng Tableaux technicke. Those last ones, in particular, resoult that are also used in the representations of the Lorentz group, because of the litle grou and all that. Young Tableaux are not particularly difficoult to understand, basically a way to represent symmetric and antisymmetric part of a tensor products. So, when I found then in string theory books as a way to represent the particle content of the strings, I understood what was going on, but lacking calculational confidence (It was not teached in my course at the university and I just had readed previously the basic ideas) always maade me feel that that calculation of the string spectrum was "goup theory maguffery". I still think that it´s is not the best way to show the physic content of the string theories so I recmend to read the corresponding chapters in the books of Polyakov and Zweibach where one can get a more deep physical idea of what´s going on.

Another ugly part of group theory, this time restricted to physicians oriented books, is the choice of examples. Some books, for example the one of Miller, makes an extensive use of examples extracted from non relativistic quantum theory. Anthoer´s, the one of Georgy, focuses more on particle physics. In fact I can´t say for sure that it is a bad thin, but one can get lost with so many "phenomenology" and loose the common points. A separate problem is the Poincaré and Lorentz groups. I still have not totally clear how important is to care about irreducible representations, which are necesarilly infinite dimensinal, and why more aspects are done with finite dimensinal ones. Maybe the lecture of the techniche of the induced representation, whch I still didn´t do, clarify me some things. I also have no clear why exactly are important in general the casimir operators of a representation. And I still have a vague idea of the role of chaaracters of representaions for Lie groups. AS the reader can deduce group theory has many aspects and it is easy to get a false idea tht some knows properly it. Fourtounately I never have felt that a not perfect understanding of some particular aspects of group theroy forbids me to understand the ideas of physic. In fact one thing that always had intrigued me, the way quarks were assigned charge was not rellated (as I thought) to conserved charges ia the Noether theorem but comes from the pauli principle (for quantum numbers difernet from spin) which dictates some prticular choice of the representation (assoiciated vector bundle in the language of geometry of fiber bundles).

But the previous things have not been my main, and more difficoult concern, these last times. Afther all my basic in math is solid (or at lest I thnk so) and, beyond the problem of tradution betwen pure math texts and physicans math texts I had not deep problmes of understanding. The thing which more problems gave tome is the renormalization group. I haad previously mentioned an entry of Distler about the modern renormalization group and it´s relation to the try of Reuters to find a non perturbative way to get a quantum gravity along the more traditinal lines of QFT. Well, Distler, and also Lubos, gave some ideas of what´s was ging there, and remarked how important it was to know the exact renormalization group equations. In fact Distler did recently two new posts about the topic. Well, that has suposed a big problem for me. I knew reasonably well the old perturbabative renormalization and the renormalizaation group of Callan-Symanzisk, and it´s role for the calculation of the running coupling constants. I also could get an intuitive idea of what is a releant, irrelevant or marginal operator. Afhter all similar cncepts are used in conformal field theory. But one thing is to have a vague idea aand another a proper understanding, so I went to the string wiki and pursued the review articles. And I got totally lost. The ultimate reason for that is that that ideas of renormalization group come from condensed matter (il.e. statiticall physic). And that is a very bad new for me. My knowledge of termodinamics and statistical physic was, well, er...average ;-). I mean, I had a right understanding of the microcanonical ensemble, whch allowed me to undersandthe meaning of entropy. I understod the role of the other ensambles and that you could get termodynamics from statisticall mechanics (and that point not quite well). The problem is that I never had understood the utility of thermodinamics (in my first contact with it was tacitally assumed that I already knew it and the focous was in it´s relation to statisticall mechanics, pitty tht I never had been teached it). Well, no problem, what really was needed was to learn statistichal mechanics, and to calculate partition functions, classical and quantum. I got used to learn about fery and bose statistic and, to be honest, not too much more. Beeing a "pure theoretic" that never worried me too much. I could, more or less follow the basic ideas I needed to u nderstand in solid state physic and I neveer cared too much. In fact I gained some better understanding of some aspectos of termodinamics, including a somewhat non stndar aspects, Ossanger relations, reading about thermodinamics in biologic procces. I also had some very vague notios about phase transitions, in the Erenfest classification.

Well, all of that tottally insuifient. Once I realized that by reading the availabe reviews I was going to nowere I decided to follow the ling way and to relearn all the thermodinamcic and statistical l hysic from the beguining. Afther that I readed the chapters of the Kerson Huang book on phase transition and renormalization group. There I learned about things such like "kadanof blocking", the meaning of fixed points and all that. But still I felt thaat I was lacking many detaills. I tried to read agian some reviews and I got more ideas, but still not eonguht. I learned that, beyond the work of Wilson, there were tow "exact renormalization group equations". The Wegner-Hougthon and the Polchinsky ones. I even tried to read the original article of Polchinsky and besides ewin advised that he was able to proof the renormalizability of the interacting sclar theory without using topology of Feynman graphs and the Weinberg therem I didn´t understand anything. Somewhat desesperated I readed the nobel price acceptance article of Wilson and I got a better idea of what it would be the path to follow. I went for a book of renormalization group and phase transitions for condensed matter phisicans. Concretely I got "lectures on phase transitions and the renormalization group" by Nigel Goldenfeld. AS I had readed in the Huang book the basic ideas of phase transitions I went directlly to the chapters on the renormalization group. I didn´t understand all the points, particularly I got a bit lost in the 10th chapter abut anomalous dimensions. But, in general, I got, at last, a felling that I am in the right waay. A problem (probably the only one in a very well written and clear book) is that it doesn´t use field theoretic (i.e. path integral) technckes. For that particular are recomended tow books, one of Collins "renormaliztion" and one form Zin-Justin "renormalization group and critical phenomena". To be honnest, afhter all this statistichal mechanics I was dissapointed to have to read just another book. So I tried to read agian one of the review articles, and this time, at last, I understood the basic ideas, and some of the detaills. Also I have beguined to catch the detaill of the relations betwen the old and new renormalization group equations. Not surprsingly I learned that there were some diferences in the aspects of the renormalization group that interest to condensed matter physics (local ones, basically to calculate critical exponents) and the aspects usefull for an particle physis (the so called global renormalization group). Althought seemenly not essenciall I decided to read the first chapters of the goldenfeld book in general phase transition theory. I must say that I am finding it a very good idea because It clarfies the concepts a lot better that the Kerson Huang´s book. Also, beeing so well writen, seems not to be a very mcuh time consuming task.

Afther that I plain to read a book (fortunately short) about conformall field theory oriented minlly to statisticall physic. I understand CFT as applied to string theory, but I guess that reading that book I am going to get a cleare ideas of many aspects, which I now understand at the formal levl, but, probably, have some subleties that I am missing now.

And while I passed all this time triying to fill some gaps Mr Lubos Motl has recommeded as "imprescindible" not one, but two articles in string theory, of 100+ pages any. And one of the articles is just the first part of another (probalby of similar size). Er, fine, it´s good to do quantum gravity, isn´t it? xD.

Anyway, if there is out there some lector who find that my actual publication rate in this blog is not fast enought I have good news for him/her. I have another journal, in livejournal, where I have published about other topics than quantum gravity. The level, and thematic, of that journal is to wide, it includes music, cinema, sci-fi and some more topics. Sitll it is mainly a physics/mathematics journal and there are some not too bad posts in this areas. I have decided to open anthoer blog (maybe in wordpress) where I will collect the better of that articles and post new ones. I prefer to rserve this blog exclusively for quantum gravity, and I guess the reader interested in physics and maths will be glad not to have to read posts of topic triying to search interesting things (I personally find annoying to read physics journals where most of the posts are not related to physic). I am sad to say, for english readers, that in that blog all, or almost all, entries will be in spanish, sorry for te inconvenience.

P.S. I have seen just now an answer in the last post that I had missed, I´ll try to answer it as son as possible.

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