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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
Abstract:
Spin Foam Models are supposed to be discretised path integrals for quantum
gravity constructed from the Plebanski-Holst action. The reason for there being
several models currently under consideration is that no consensus has been
reached for how to implement the simplicity constraints. Indeed, none of these
models strictly follows from the original path integral with commuting B
fields, rather, by some non standard manipulations one always ends up with non
commuting B fields and the simplicity constraints become in fact anomalous
which is the source for there being several inequivalent strategies to
circumvent the associated problems. In this article, we construct a new
Euclidian Spin Foam Model which is constructed by standard methods from the
Plebanski-Holst path integral with commuting B fields discretised on a 4D
simplicial complex. The resulting model differs from the current ones in
several aspects, one of them being that the closure constraint needs special
care. Only when dropping the closure constraint by hand and only in the large
spin limit can the vertex amplitudes of this model be related to those of the
FK Model but even then the face and edge amplitude differ. Curiously, an ad hoc
non-commutative deformation of the $B^{IJ}$ variables leads from our new model
to the Barrett-Crane Model in the case of Barbero-Immirzi parameter goes to
infinity.
