Mathematical framework of lqg against string theory?

[MathematicalPhysicist]

what the differences in the mathematical framework in the two theories?
i know i heard that the maths of string theory is of 21th century (which is now).

 

[MathematicalPhysicist]

because no one answered i have asked in the superstringtheory.com about the framework of string theory.
hope that answers will be given.

 

[jeff]

You can't really talk about the "mathematical framework" of strings like you can with LQG. Like typical canonical approaches to the QG problem, LQG proceeds on the assumption that basing a quantum theory of gravity directly on the classical phase space and lagrangian of GR is valid right down to the Planck scale. This means that LQG is mathematically quite simple. In fact anyone that's completed one good graduate level course in each of QFT and GR will not need to upgrade their mathematical knowledge much to understand most LQG papers.

String theory on the other hand is a different animal altogether. For example, it's a unified theory of all interactions, not just gravity, it postulates the existence of more than three spatial dimensions in which live fundamental bodies extended in up to nine of them, and it's a supersymmetric theory.

This gives rise to an enormous variety of phenomena that require a similarly enormous variety of mathematical techniques to describe. Hence a great deal of mathematical study beyond what you'd see in even the most advanced physics courses is required to understand string theory. Further, LQG is a more or less closed theory by which I mean there's no evidence within it that there's a deeper theory of which LQG is only an approximation. Not so with string theory. We know for a fact that it's just a scratch on the surface of an all encompassing theory called M-theory, and moving towards it has required new mathematical techniques with the efforts to produce them becoming an important driving force in pure mathematics. So the mathematical framework of string theory is much broader than LQG and continues to expand at a pretty good clip.

Needless to say you probably won't see much discussion of string theory in this forum for quite a while - if ever - since the learning curve is so steep.

 

[selfAdjoint]

Here's a review paper on Loops versus Strings

 

[jeff]

Originally posted by selfAdjoint
Here's a review paper on Loops versus Strings

String theory is immeasurably deeper than LQG and this paper reflects that a bit more than others that have been recommended. The point is also made that any theory with a fundamental scale automatically predicts dispersion effects like those discussed in the context of LQG where such effects are attributed to it's modelling of spacetime geometry as being discrete.