Strings and non-commutative qft

[naunzer]

I've sometimes heard that there are string theory results that are quite
similar to some of non-commutative qft.
What are these?

 

[humanino]

Welcome naunzer !

what do you call "non-commutative qft" ? This is confusing. Is this Connes' geometry ?

 

[naunzer]

Yes, I think it was A. Connes who thought about it first.
But is it now called nc-geometry or nc-quantum field theory(nc-qft).

 

[humanino]

I can't help much. I want to say that I picture Connes' work as very much more fundamental than anything else that has been done for decades. He basically claims that we did not take seriously enough the fundamental observations of QM. I mean to say that, he probably does not care about reproducing stringy theories. I know that the standard model has been translated in his geometry, and this is (in my opinion) by far the most elegant formulation of physics available.

Unfortunately : I do understand some of string theories or LQG, and I do have Connes' book, and began it. But I preferred to postpone this reading, because it is way more mathematical than everything else, and will require me full-time attention.

 

[naunzer]

I've read a bit in Nakahara' s "Geometry, Topology and Physics" and at the
end there is a chapter string theory where he uses Atiyah's index theorems and
those Chern class things etc.
I found that very mathematical, too.
So maybe you can tell me,
what are the mathematical preliminaries for string theories and for LQG?
Are these (Nakahara's) attemps to formulate things in a "more mathematical" sense, because in the Green, Schwarz, Witten - book those things are not used (at least in the beginning of part I).

 

[humanino]

check [thread=27544]this[/thread] I am not competent here.

 

[naunzer]

Thank you very much. I will check it.

 

[sol2]

These are good questions and I certainly appreciate them

I have to go back to some early conversations here in this regard so bear with me. I will be using you links to correct my thinking and at the same time project ahead of your conversation.

I expressed the use of a Toy Model for consideration using the vacuum of space and how we might percieve brane worlds. So immediately one is drawn t the first statement in bold, in link supplied.

In quantum mechanics, the vacuum of space is not a vacuum; rather, it is field with virtual particles, such as the graviton. Light passing through this field of virtual particles is refracted, just as it is when passing through water or any medium.

The graviton, being the essence of gravitational force, would interact with (or slow down) those particles with greater gravitational potential. With mass directly proportional to energy, as expressed in e=mc2, photons of higher energy have greater gravitational potential than lower-energy photons -- as if they "weigh" more.

The highest-energy photons would therefore travel through space more slowly than lower-energy photons. (This does not violate the constancy of the speed of light, for light travels at the same speed only in an absolute vacuum.) To detect the very slight difference in photon speed, one needs an extremely distant source emitting extremely high-energy photons: that is, the gamma ray burst.

http://www.astronomytoday.com/cosmology/quantumgrav.html

I was looking for some method that would help me discern the nature of this quantum geometry, yet it has revealled a non communitive geometry for thinking, so this begins a new road.

It must be recognized tha LQG does not recognize the graviton, yet strings does. So looking to SR I see where LQG is basing its bets?

I hope this falls in line with your post.

https://www.physicsforums.com/showpost.php?p=255354&postcount=2

Now for some of you who understand the vacuum we are looking for how such potentials of the gauss field could have been limited to the event, and how we might have interpreted the energy leaking into those extra dimensions?

Each cosmological event has a "distance function" to it, that is revealled in the scalar product. Now for geometricization to take hold here, it had to recognize the energy values of those events and how photon recognition could point to the dynamics unfolding. This in itself is pointing to the geometrication of the cosmo, as well as quantifing the gravitational consideration of these events. This should be pretty clear by now.

If such a membrane is visualized as as been shown here, you get the sense of how the comos is showing itself in those same brane collisions, cosmo events held to the brane. These are fermion considerations that are being seen, and for bosons(graviton) we know these are not being held to the brane.

So quantization of gravitational waves sets the thinking in how dynamical that bulk is, and in the presence of these quanticized geometricization, we learn how the photon can react.

One would have to understand the shell approach. Limininocentric structures are very revealing in this regard as well as pelastrian views. Understanding this geometry greatly helps to undertand the topological events that are unfolding in the cosmo.

The basis of this post helps resolve https://www.physicsforums.com/showthread.php?goto=newpost&t=42840 Nereid's in astronomy today

As always, I am open for corrections.

 

[arivero]

I can't help much. I want to say that I picture Connes' work as very much more fundamental than anything else that has been done for decades.

(...)

Unfortunately : I do understand some of string theories or LQG, and I do have Connes' book, and began it. But I preferred to postpone this reading, because it is way more mathematical than everything else, and will require me full-time attention.

I Fully agree with your oppinion.

From your location (Paris) it seems you could get some hint by going to Connes's lectures. The red book is uneasy to read: the french book is a little bit more amenable.

As for nc-field theories, it is not clear how they are related to Connes NCG. At least, there are some papers showing that Moyal products can be formulated in Connes formalism. But nc-field workers do not worry, generally, about making connections with it. This is different from quantum-groups, which Fadeev has always interpreted as a loosy version of Connes duality between manifolds and algebras.

 

[humanino]

Thanks arivero. I have no time to go to Connes' lecture, because I am involved in my PhD. I deeply regret that of course. I will consider buying or renting the french version of Connes' book, also because of ([thread=41006]in "spectral triples and critical dimension"[/thread]) :

During my travel, I have remembered a related point: Dixmier trace has
a kind of scale invariance; this was remarked in the French version of the
book of Alain Connes, but de-emphatised in the english one. I will try to
think along this line.

Maybe other modifications have been done. It will also be easier for me in french. Paperback & english book are so cheap in the US.