Even if string should turn out to be a dead end as far as unification goes, and fail to produce a predictive theory of how the world works, it could still be interesting and constructive to formulate some version of string within the background independent LQG context. Here is a recent paper which addresses that challenge.(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/0908.0953

Canonical Analysis of the Algebraic String

Winston J. Fairbairn, Karim Noui, Francesco Sardelli

And here is a quote from the conclusions section of the paper:

"One of the main aspects that strikes us with the algebraic string is its numerous similarities with the Ashtekar formulation of gravity. It is a ﬁrst order formulation, it is of course diﬀeomorphism invariant, and admits an Immirzi type parameter. All these aspects makes the system a very nice arena to test the ideas and techniques of Loop Quantum Gravity (LQG). Indeed, the system is very interested in itself and simple enough to be completely quantised. The Fock quantisation already partially exists. Our aim, in future work, is to develop a background independent quantisationin order to conclude on the equivalence or not with the Fock quantisation.à la LQG

This idea was in fact initiated by Thiemann [14] in the context of the Nambu-Goto string but we think that the algebraic formulation of the string is more suited for that speciﬁc problem. Furthermore, there is an Immirzi-type parameter and then we hope to understand its eﬀects in the quantum theory. We hope the algebraic string helps us to understand some other fundamental aspects of LQG. For instance, we can ask the question if this formulation can lead us to a Spin-Foam [20] formulation of the string.

If this is the case, we have a new arena, simpler than gravity, to understand the

link between the covariant and canonical quantisations of background independent

theories.

In brief, the next step is the compare the quantisations of the algebraic stringà la LQGvs.à la Fock. We are currently working in that direction."

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# String in a LQG context

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