642 research outputs found
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
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
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 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
Group field theory with non-commutative metric variables
We introduce a dual formulation of group field theories, making them a type
of non-commutative field theories. In this formulation, the variables of the
field are Lie algebra variables with a clear interpretation in terms of
simplicial geometry. For Ooguri-type models, the Feynman amplitudes are
simplicial path integrals for BF theories. This formulation suggests ways to
impose the simplicity constraints involved in BF formulations of 4d gravity
directly at the level of the group field theory action. We illustrate this by
giving a new GFT definition of the Barrett-Crane model.Comment: 4 pages; v3 published versio
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
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