Tuesday, April 29, 2008

Gerard ’t Hooft: A diferent string theory

The first oe paper is LOCALLY FINITE MODEL FOR GRAVITY written by Gerard ’t Hooft. If by some casual you dont know who ´t hoof is just to say that he has a nobel prize by proving that the gauge theories, wich are the basic ingredient, of the standard model, are renormalizable. A few physicists I know consider him the last greater phyisicist (Steven Weinberg would be considered slighly earlier in time). ON the other hand be sure that Lubos Motl is not among his fans ;-). Ok, let´s leave sociology and go into physic. The abstract of the paper is this:

Matter interacting classically with gravity in 3+1 dimensions usually gives
rise to a continuum of degrees of freedom, so that, in any attempt to quantize
the theory, ultraviolet divergences are nearly inevitable. Here, we investigate
matter of a form that only displays a finite number of degrees of freedom
in compact sections of space-time. In finite domains, one has only exact,
analytic solutions. This is achieved by limiting ourselves to straight pieces of
string, surrounded by locally flat sections of space-time. Globally, however,
the model is not finite, because solutions tend to generate infinite fractals.
The model is not (yet) quantized, but could serve as an interesting setting
for analytical approaches to classical general relativity, as well as a possible
stepping stone for quantum models. Details of its properties are explained,
but some problems remain unsolved, such as a complete description of the
most violent interactions, which can become quite complex.

The paper begins with some considerations about 2+1 dimensions and the role of pont partile matter as source of curvature, in the form of a wedge in space time. Inspired by that view he considers the extension of this to 3+1 dimensions. The role of the point particles are now strings. Why? Simply because the aditional dimension is perpendicular to the others and so a point becomes an infinite string. In principle it could look a bit arbitrary, and not general. But the idea seems to consider the space-time sourruounding that infinite strings.

He writes the energy momentun tensor for that strings (well known for people aware of cosmic strings). Later he considers moving and interacting strings. In considering this he concerns about holonomy so maybe the reader would consult something about this topic if he does´nt know it previously. The wikipedia entry is specially good about the topic so it could be a quick start guide. The very quick idea of homotopy is to consider a map betwen parallel transport of vectors around a closed curve and the group associated to the bundle (wich defines the very concept of paralell transpoort).

Afther that he considers interactions of strings. The first claim is as a resoult of interactions, connections, he cant´consider infinite strings alone anymore. Diferent types of collisions are analized. He cnsiders vaious posibilities and takes care about some possible issues (for example, rotating strings would create spacetimes with closed timelike curves as is well known since the work of Gott). I am not sure of how much of this work would intersect with the well stablished resoults about networks of cosmic strings (gauge or superstring ones). It would be fine if some reader would know it and could say something about it.

The final conclusion he claims is that he can get all the degrees of freedom of gravity by pieces of straight strings. In this way he could study gravity just from this. Seemengly this is somewhat similar to Regge calculus (a discretized aproach to quantum gravity)using strings instead of points in the nodes. He also says that in this sense is just the opposite to some papers triying to get matter from ure gravity (in a clear reference to Smollin program in the octopy). In the paper a quantizaion of the model is not made, that is announced for a future paper. About that paper he says that he will not follow traditional quantiztion proceduers based in lagrangian mechanisms,partially because the model seems not to admit a Lagrangian formulation). AS an advance a claim is made that the theory will not have ultraviolete divergences but possibly will have problems with infrared regime.

Well, I still have to re-read carefully some pieces of the paper, and a definite juice will only be possible when the paper on quantization would be available. Also it would be interesting to see how it is recived by the mainstream physic comunity. For example Sean carroll has announced that he will speak about the paper (it is how I knew about it´s existence). And, I guess that also Lubos Motl will have something to say, given his aparent animosity against t' hoof (maybe because he has sometimes soped favourably about the LQG comunity). Personally I consider ’t Hooft a very interisting figure and I like to be aware of what he does, even if I don´t necesarilly agree with all his conclusions.

No comments: