Baez and Perez beef strings and branes

[Careful]

**
The easiest thing to describe is the "moduli space of flat G-bundles" over any connected manifold M. Points in this are gauge equivalence classes of G-bundles with flat connection over M. This space turns out to be **


Thanks for providing this information which will allow many people here to better understand the context in which to see this work.

Cheers,

Careful

 

[marcus]

...

Thanks for providing this information which will allow many people here to better understand the context in which to understand this work.
...

Compliments on your side as well, Mr. Careful.

 

[Careful]

Compliments on your side as well, Mr. Careful.

Well, I must confess I passively knew this classification result but it got kind of in some more distant part of my memory. Hence, it was useful for me too in that respect (and nothing is better than an explanation by a good mathematical physicist who is actively doing this particular stuff).

 

[Mike2]

Category theory is a general language for describing things and
processes - called "objects" and "morphisms". In this language,
the counterintuitive features of quantum theory turn out to be
properties that the category of Hilbert spaces shares with the
category of cobordisms - in which objects are choices of "space",
and morphisms are choices of "spacetime". The striking similarities
between these categories suggests that "n-categories with duals"
are a promising framework for a quantum theory of spacetime.
We sketch the historical development of these ideas from Feynman
diagrams, to string theory, topological quantum field theory, spin
networks and spin foams, and especially recent work on open-closed
string theory, quantum gravity coupled to point particles, and 4d
BF theory coupled to strings.

I wonder if there is an merit to the idea of a category where the objects ARE the morphisms. I'm thinking that in the very very early universe, when the universe was just a single particle (?), was the universe then an object or a process? Perhaps the two were indistinguishable at that point. I'm also thinking in terms of QCD where the particles (objects?) that give rise to the forces (processes?) are indistinquishable, the force carrier is the same as the particle being forced, IIRC. Any thoughts along these lines? Would this be the "dual" that you mention above? Thanks.

 

[Kea]

I wonder if there is any merit to the idea of a category where the objects ARE the morphisms.

Actually, objects are really identity arrows, so everything is a morphism. The correspondence you propose, however, is too simplistic. Physically, an origin to a classical universe must be a complex entity - a morphism, sure, like everything, but one needs to understand exactly what kind, and this is not a simple question.

The duals might be dual Hilbert spaces, in the usual sense, or at a much deeper level, String type duals.

 

[marcus]

BTW Alejandro Perez will be in Utrecht in a few days giving a talk on the subject of this paper

the current seminar schedule is here
http://www.phys.uu.nl/~loll/Web/seminars/seminars.html

the date and title of the talk is

May 29 Alejandro Perez (Marseille): Quantization of strings and branes coupled to BF theory