Kisielowski Lewandowski Puchta have made a significant advance in calculating the transition amplitudes between quantum states of geometry.(adsbygoogle = window.adsbygoogle || []).push({});

They have found a systematic algorithm that enumerates the (generalized) spinfoam-like histories by which one state evolves into another.

And in this case the amplitude of each history is conveniently accessible. Each history that one enumerates more or less "comes with" its probability amplitude.

This looks to me like a systematic combinatorial algorithm that can be PROGRAMMED, which is one reason it's potentially important.

In the September 2011 seminar discussion Laurent Freidel objected that the algorithm does not offer any advantage in the case where one restricts to spinfoams which are dual to triangulations of a 4d manifold. (The vertices at most 5-valent etc.)

But Frank Hellmann (AEI) countered by observing that one HAS to consider more general spinfoams because they, for example, arise naturally in the simplest applications to cosmology. He and co-workers have been studying the "hourglass" spinfoam picture of the cosmological bounce and have found they have to go to cases which are not based on triangulations He reported that they had found the Warsaw algorithm a big help.

Our two sources on this are the paper http://arxiv.org/abs/1107.5185 and the online recorded seminar talk by Puchta.

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# Feynmans of geometry: computable trans. amps. by K+Le+P algorithm

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