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Science Advisor

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## Main Question or Discussion Point

In http://arxiv.org/abs/1010.1939, Eq 26 & 27, Rovelli used 2 limits to define the current spin foam models. But he doesn't know if those limits exist.

In http://arxiv.org/abs/1010.5437, Rovelli and Smerlak further elaborated properties of the limits, assuming their existence.

Frank Hellmann commented on them in http://arxiv.org/abs/1105.1334

"The refinement limit considered in [RS10] envisions going to an “infinite complete 2-complex” and thus is of a significantly different nature. ... We would also expect that in the case of gravity we will not be able to define the refinement limit exactly, but only approximately ...

A new comment has appeared in Kisielowski, Lewandowski, and Puchta's http://arxiv.org/abs/1107.5185

"One of the open problems of the spin foam approaches to the 4D gravity is definition of the total amplitude that takes into account all the foams. A recent breakthrough in this issue is Rovelli-Smerlak’s projective limit definition [28]. How do our diagrams fit in this limit?

I've bolded the statements above which refer to unpublished work. I await these developments with bated breath

In http://arxiv.org/abs/1010.5437, Rovelli and Smerlak further elaborated properties of the limits, assuming their existence.

Frank Hellmann commented on them in http://arxiv.org/abs/1105.1334

"The refinement limit considered in [RS10] envisions going to an “infinite complete 2-complex” and thus is of a significantly different nature. ... We would also expect that in the case of gravity we will not be able to define the refinement limit exactly, but only approximately ...

**In the case of general spin foam models Bahr has suggested a set of cylindrical consistency conditions [Bah].**"A new comment has appeared in Kisielowski, Lewandowski, and Puchta's http://arxiv.org/abs/1107.5185

"One of the open problems of the spin foam approaches to the 4D gravity is definition of the total amplitude that takes into account all the foams. A recent breakthrough in this issue is Rovelli-Smerlak’s projective limit definition [28]. How do our diagrams fit in this limit?

**Those questions will be answered soon either by us or by the readers.**"I've bolded the statements above which refer to unpublished work. I await these developments with bated breath

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