The Feynman propagator for spin foam quantum gravity

Details The Feynman propagator for spin foam quantum gravity The Feynman propagator for spin foam quantum gravity

2004-10-27

arxiv.org/abs/gr-qc/0410134v3

Phys.Rev.Lett. 94 (2005) 111301

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTex, 5 pages, no figures; v2-3:minor typos corrected

Scientific paper

10.1103/PhysRevLett.94.111301

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''.

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