David Finkelstein's no-field theory

[selfAdjoint]

Has anyone seen http://arxiv.org/PS_cache/gr-qc/pdf/0608/0608086.pdf" new paper by David Finkelstein at Georgia Tech?

He claims a new method of quantization through "homotopic flexing" (his new-coined term) of Lie Groups, and the paper includes many goodies, such as only histories are really observable, as Dirac, Schwinger, and Feynman understood but Heisenberg muffed on. But quantized histories are highly nonsingular and ill-defined (e.g. path integration, or see Lubos Motl on spin-foam formalism). BUT, Finkelstein's new flex algebra method replaces crude "flat" algebras which can't handle histories with larger dimensional flexible algebras which have no problem with them.

Finkelstein admits he "stops halfway" in this paper because he quantizes gravity but not with matter (welcome to the club!). Nevertheless, this is a refreshing new way of looking at things.

 

[marcus]

Has anyone seen http://arxiv.org/PS_cache/gr-qc/pdf/0608/0608086.pdf" new paper by David Finkelstein at Georgia Tech?
...

he has a Wikipedia entry with a bit of bio.
http://en.wikipedia.org/wiki/David_Finkelstein

his page at Georgia Tech has a picture and a discussion of
http://www.physics.gatech.edu/people/faculty/dfinkelstein.html
some of his main ideas: quantized time, "universal relativity".
some of his ideas seem very original.
glad you called attention to him.
he likes to use the Clifford algebra (conceivably could be an idea or two in his head that Garrett could use, never can tell)

 

[Farsight]

Can anybody make an attempt to summarize the gist of this?

 

[selfAdjoint]

Can anybody make an attempt to summarize the gist of this?

Instead of doing it all off the top of my head I'm going to read the paper some more and get back to you. I want to learn it too. But his idea of "flexing" a Lie group boils down to this. There are a skillion different groups out in what they call "group space" which is just math-speak for the set of all the Lie groups there are. So suppose we have such a group given to us by the physics, and suppose it causes us headaches. Finkelstein refers to such a group as "flat", suggesting flat Minkowski spacetime versus curved GR spacetime, or maybe even flat Earth versus round Earth.

So he proposes to go by way of a homotopy, a smooth transition path through the space of Lie groups, from the "flat" one to a more "flexible" one, that because of the nice properties of the homotopy he wants to use, is akin to the flat one, but free of some of the headaches that came of the flatness. And among the problems he says he can clear up by doing this is the problem of rigorously defining and using the sum over history technique, which physicists commonly address with not much better than hand waving because the given gauge groups are (so Finkelstein says) flat, and not up to the job of handling sums over histories.

 

[f-h]

Is there a natural topology on group space?

Edit:
Ah I see he works with the space of Lie Algebras, parametrized by the space of structure functions...

 

[garrett]

Ah I see he works with the space of Lie Algebras, parametrized by the space of structure functions...

Isn't that the same as a Lie algebra deformation?

Guess I'll read the paper...

 

[Chronos]

I like the flexing idea. It portrays a universe that is flat on average [a global thing] but rife with local curvature. The math is pretty difficult [at least for me], but that was my read.