String treatment of the quantum graphity model

[dhillonv10]

Hi all,

I recently read about the quantum graphity model that was proposed by Lee Smolin et. al. The model had some really nice features but can anyone tell me if a similar string based model has been proposed? I know that string net condensation does something similar but has a full model ever been proposed? Links to any papers will be much appreciated. Thanks.

 

[weburbia]

It depends what you mean by "similar".
If you mean a model where space is emergent then any of the well known Matrix String Theories would count.
If you mean something using the idea that permutation symmetry over points in space or events in spacetime is a fundamental symmetry try http://inspirebeta.net/record/454519?ln=en or http://arxiv.org/abs/hep-th/9802085.
If you mean something based on random graphs try http://arxiv.org/abs/hep-th/0010126
If you mean something else please give more specifics.

 

[dhillonv10]

Thanks for your quick reply weburbia, I wasn't specific in my post because I didn't know the different types, I am looking for a model that can serve as a sort of bridge allowing me to use the results presented in the quantum graphity paper in a string theory context. Does that perhaps help? Actually http://arxiv.org/abs/hep-th/0010126 may be it :) thanks again.

 

[Kevin_Axion]

http://en.wikipedia.org/wiki/Event_symmetry#Event_symmetry_and_string_theory

 

[dhillonv10]

thanks for your reply Kevin, I've read that page before :) perhaps I should rephrase my question...

 

[dhillonv10]

I must apologize Kevin, I never read this section carefully, thanks for the link and thanks to everyone for their help.

 

[Kevin_Axion]

No problem :).

 

[dhillonv10]

Kevin: I am still have some trouble relating event symmetry to random graph models, I got the answer I was searching for, string theory is shown to contain event symmetry which allows me to use the idea of graphs from the quantum graphity paper into string theory context but what does event symmetry have to do with random graphs? Thanks.

 

[weburbia]

Event Symmetry means that there is an invariance under permutations of space-time events in some pregeometric model. This is taken to be a generalisation of diffeomorphism invariance which uses more restricted mappings of spacetime events on manifolds.

If the nodes in a random graph model are interpreted as spacetime events and the random dynamics respect the permutation symmetry then you can say that it is an event-symmetric random graph model of spacetime.

In quantum graphity the nodes are interpreted as points in space rather than events in spacetime but the permutation symmetry is still there and the general idea is similar.

 

[qsa]

can anybody see a relation to this paper





http://arxiv.org/PS_cache/arxiv/pdf/...105.3930v1.pdf

The emergence of Special and Doubly Special Relativity
Authors: Petr Jizba, Fabio Scardigli
(Submitted on 19 May 2011)
Abstract: In a previous paper [Phys.Rev.D82, 085016(2010)] we introduced a method for obtaining the exact Feynman propagator of a relativistic particle (for both Klein-Gordon and Dirac case) from a superstatistical average over non-relativistic single-particle paths. We suggested that this method could offer new insights into the currently much debated issue of emergent relativity. In this paper we proceed further, showing that a Brownian motion on a short scale originates a relativistic motion on scales larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. We also present the modifications necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, an unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as generalized canonical commutation relations, connection with Feynman chessboard model, and Hausforff dimensions of corresponding path-integral trajectories are also discussed.




or maybe this





http://icgem.gfz-potsdam.de/GR/QM-Publication.pdf

Here I present a new discrete model of quantum mechanics for relativistic
1-electron systems, in which particle movement is described by a
directed space-time graph with attached 4-spinors, but without any continuous
wave functions. These graphs only consist of few space-like edges,
e.g. the ground state of atoms is described by two nodes and one edge,
and interactions only take place at the nodes.
The fundament is an extremal principle for a relativistic invariant
“lagrangian sum”, from which “field-equations” and “equations of motion”
are derived, so the states (including the graph nodes) are completely
determined.
As important validations of the model, the corresponding graphs for
the stationary Dirac-equation for the atom are drawn and the correct
spectra are computed (Sommerfeld-levels).
Also a discrete schr¨odinger approximation and an associated
“hamiltonian sum” are derived and the correct equation of a classical
moving particle under Lorentz-force is presented.
I hope, that this new approach will help, to overcome some problems
of current quantum mechanics by making the wave function superfluous.