# Trying to learn Spinf Foams and a lot of questions

1. Dec 8, 2009

### zwicky

Hi everybody!!

To point, I'm studying the paper of Perez (http://arxiv.org/PS_cache/gr-qc/pdf/0402/0402110v3.pdf) in at the end of page 12 can be read something like
$$\sum_{j_p}(2j_{j_p}+1)<\prod_p\chi_{j_p}(U_p)s,s'>=<\prod_{j_p}\sum_{j_p}(2j_{j_p}+1)\chi_{j_p}(U_p)s,s'>$$

My question is, which is the trick to interchange the prod by the sum? I know that the the prod on the r.h.s runs in j_p instead of p, but still I'm not sure about it.

Thanks in advance guys

Z.

P.D. If someone knows about an introduction with detailed calculations to this fascinating subject besides the the well know Baez or Perez reviews, "my gratitude would know no bounds".