Imaginary time in spin foams

[atyy]

In Q (http://www.einstein-online.info/spotlights/path_integrals)M (http://books.google.com/books?id=Bn7MaT3X8fkC&source=gbs_navlinks_s) and QFT (http://arxiv.org/abs/hep-lat/9807028), imaginary time is used to make the oscillatory path integral converge, and also to handle terms that are not semibounded in Minkowski spacetime.

In CDT, imaginary time is also used after the path integral is restricted to "causal" configurations.

How is the oscillatory term handled in spin foams?

[genneth]

Is this not the point of Euclidean spin-foams?

[atyy]

Is this not the point of Euclidean spin-foams?

Looking in Perez's notes (http://arxiv.org/abs/gr-qc/0301113), Eq 27 for a Euclidean spin foam, it looks like he still has the i in the path integral. I guess the Euclidean means that it produces a geometry with Euclidean signature (I guess he takes only one of the two imaginary time replacements)?