Non-commutative quantum geometric data in group field theories

We review briefly the motivations for introducing additional group-theoretic data in tensor models, leading to the richer framework of group field theories, themselves a field theory formulation of loop quantum gravity. We discuss how these data give to the GFT amplitudes the structure of lattice gauge theories and simplicial gravity path integrals, and make their quantum geometry manifest. We focus in particular on the non-commutative flux/algebra representation of these models.Comment: 10 pages; to appear in the proceedings of the workshop "Non-commutative field theory and gravity", Corfu', Greece, EU, September 201

No alternative to proliferation

We reflect on the nature, role and limits of non-empirical theory assessment in fundamental physics, focusing in particular on quantum gravity. We argue for the usefulness and, to some extent, necessity of non-empirical theory assessment, but also examine critically its dangers. We conclude that the principle of proliferation of theories is not only at the very root of theory assessment but all the more necessary when experimental tests are scarce, and also that, in the same situation, it represents the only medicine against the degeneration of scientific research programmes.Comment: 15 pages; contribution to the volume "Why trust a theory?", edited by: R. Dardashti, R. Dawid, K. Thebault, to be published by Cambridge University Pres

The quantum geometry of tensorial group field theories

We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum spacetime. We also review briefly some recent results concerning the definition of such pre-geometric content, and of models incorporating it.Comment: 6 pages; uses ws-proc style; contribution to the proceedings of The XXIX International Colloquium on Group-Theoretical Methods in Physics, August 20-26, 2012, Chern Institute of Mathematics, Tianjin, Chin

The Feynman propagator for quantum gravity: spin foams, proper time, orientation, causality and timeless-ordering

We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate causal structure in the orientation of the spin foam 2-complex and the data that characterize it; we construct a generalised version of spin foam models introducing an extra variable with the interpretation of proper time and show that different ranges of integration for this proper time give two separate classes of spin foam models: one corresponds to the spin foam models currently studied, that are independent of the underlying orientation/causal structure and are therefore interpreted as a-causal transition amplitudes; the second corresponds to a general definition of causal or orientation dependent spin foam models, interpreted as causal transition amplitudes or as the Quantum Gravity analogue of the Feynman propagator of field theory, implying a notion of ''timeless ordering''.Comment: 8 pages; to appear in the Proceedings of the DICE 2004 Workshop "From Decoherence and Emergent Classicality to Emergent Quantum Mechanics

The microscopic dynamics of quantum space as a group field theory

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on recent results obtained in this approach and related open issues, concerning both the mathematical definition of GFT models, and possible avenues towards extracting interesting physics from them.Comment: 60 pages. Extensively revised version of the contribution to "Foundations of Space and Time: Reflections on Quantum Gravity", edited by G. Ellis, J. Murugan, A. Weltman, published by Cambridge University Pres