MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

To make it simple, take the spin foam formalism of ($SU(2)$) 3D gravity. My question is about the choice of the data that will replace the (smoothly defined) fields $e$ (the triad) and $\omega$ (the connection) on the disretized version of space-time $\mathcal{M}$: the 2-complex $\Delta$: why choose to replace $e$ by the assignment of elemnts $e\in su(2)$ to each 1-cell of $\Delta$, and elements $g_{e}\in SU(2)$ to each edge in the dual 2-complex $\mathcal{J}_{\Delta}$? I mean, these are both $su(2)$-valued 1-forms, thus, roughly speaking, assigning elements of $su(2)$ to vectors of the tangent bundle $\mathcal{TM}$, in other terms assigning elements of $su(2)$ to infinitesimal displacements represented by the 1-cells of $\Delta$. I can understand the choise for $e$, but not for $\omega$, why this is so? Why it is not the inverse choice?

share|cite|improve this question
What is $\mathcal{J}_\Delta$? That may help people answer this. But note that this question may not attract much attention here. Wait and see. – David Roberts Dec 2 '11 at 2:34
I edited the question to specify all the symbols contained therein – Pedro Dec 2 '11 at 10:39
Are you referring to a particular paper or set of papers here as a reference? You might also have more luck on the theoretical physics stackexchange. – j.c. Dec 2 '11 at 17:12
Yes, for example, I also posted the question in thanks. – Pedro Dec 2 '11 at 23:42

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.