The Feynman propagator for spin foam quantum gravity

Abstract

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''.

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

References in corpus (8)

• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Asymptotics of Relativistic Spin Networks
• The projector on physical states in loop quantum gravity
• Sum-over-histories origin of the composition laws of relativistic quantum mechanics and quantum cosmology
• Quantum causal histories
• Implementing causality in the spin foam quantum geometry
• A Ponzano-Regge model of Lorentzian 3-Dimensional gravity
• Simple Spin Networks as Feynman Graphs

Cited by in corpus (23)

• Loop Quantum Cosmology: A Status Report
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Loop Quantum Cosmology and Spin Foams
• A spin-foam vertex amplitude with the correct semiclassical limit
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Causality and matter propagation in 3d spin foam quantum gravity
• Lorentzian quantum cosmology goes simplicial
• Semiclassical regime of Regge calculus and spin foams
• Decoherence in Quantum Gravity: Issues and Critiques
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Generalised group field theories and quantum gravity transition amplitudes
• Two-point functions in (loop) quantum cosmology
• Group field theory and simplicial quantum gravity
• Coupling of spacetime atoms and spin foam renormalisation from group field theory
• Topological lattice field theories from intertwiner dynamics
• Encoding simplicial quantum geometry in group field theories
• Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation
• Spinfoams: Foundations
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Causal structure in spin-foams
• A note on the spinor construction of Spin Foam amplitudes
• Transition probability spaces in loop quantum gravity
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model