2004/10/31 by Daniele Oriti · 1 citation
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevlett.94.111301
published as Phys.Rev.Lett. 94 (2005) 111301 · RevTex, 5 pages, no figures; v2-3:minor typos corrected
arxiv created 2005/04/19 · arxiv updated 2009/12/01
We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence. Using the technology of evolution kernels for quantum fields/particles on Lie groups/homogeneous spaces, we construct a generalised version of spin foam models, introducing an extra proper time variable and prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of QFT or as a covariant definition of the inner product between quantum gravity states; and a new class of causal models, corresponding to the quantum gravity analogue of the Feynman propagator in QFT, non-trivial function of the orientation data, and implying a notion of ''timeless ordering''.