264 research outputs found
Quantum gravity as a group field theory: a sketch
We give a very brief introduction to the group field theory approach to
quantum gravity, a generalisation of matrix models for 2-dimensional quantum
gravity to higher dimension, that has emerged recently from research in spin
foam models.Comment: jpconf; 8 pages, 9 figures; to appear in the Proceedings of the
Fourth Meeting on Constrained Dynamics and Quantum Gravity, Cala Gonone,
Italy, September 12-16, 200
Encoding simplicial quantum geometry in group field theories
We show that a new symmetry requirement on the GFT field, in the context of
an extended GFT formalism, involving both Lie algebra and group elements,
leads, in 3d, to Feynman amplitudes with a simplicial path integral form based
on the Regge action, to a proper relation between the discrete connection and
the triad vectors appearing in it, and to a much more satisfactory and
transparent encoding of simplicial geometry already at the level of the GFT
action.Comment: 15 pages, 2 figures, RevTeX, references adde
Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
We offer a perspective on some recent results obtained in the context of the
group field theory approach to quantum gravity, on top of reviewing them
briefly. These concern a natural mechanism for the emergence of non-commutative
field theories for matter directly from the GFT action, in both 3 and 4
dimensions and in both Riemannian and Lorentzian signatures. As such they
represent an important step, we argue, in bridging the gap between a quantum,
discrete picture of a pre-geometric spacetime and the effective continuum
geometric physics of gravity and matter, using ideas and tools from field
theory and condensed matter analog gravity models, applied directly at the GFT
level.Comment: 13 pages, no figures; uses JPConf style; contribution to the
proceedings of the D.I.C.E. 2008 worksho
Local gauge theory and coarse graining
Within the discrete gauge theory which is the basis of spin foam models, the
problem of macroscopically faithful coarse graining is studied. Macroscopic
data is identified; it contains the holonomy evaluation along a discrete set of
loops and the homotopy classes of certain maps. When two configurations share
this data they are related by a local deformation. The interpretation is that
such configurations differ by "microscopic details". In many cases the homotopy
type of the relevant maps is trivial for every connection; two important cases
in which the homotopy data is composed by a set of integer numbers are: (i) a
two dimensional base manifold and structure group U(1), (ii) a four dimensional
base manifold and structure group SU(2). These cases are relevant for spin foam
models of two dimensional gravity and four dimensional gravity respectively.
This result suggests that if spin foam models for two-dimensional and
four-dimensional gravity are modified to include all the relevant macroscopic
degrees of freedom -the complete collection of macroscopic variables necessary
to ensure faithful coarse graining-, then they could provide appropriate
effective theories at a given scale.Comment: Based on talk given at Loops 11-Madri
Coupling of spacetime atoms and spin foam renormalisation from group field theory
We study the issue of coupling among 4-simplices in the context of spin foam
models obtained from a group field theory formalism. We construct a
generalisation of the Barrett-Crane model in which an additional coupling
between the normals to tetrahedra, as defined in different 4-simplices that
share them, is present. This is realised through an extension of the usual
field over the group manifold to a five argument one. We define a specific
model in which this coupling is parametrised by an additional real parameter
that allows to tune the degree of locality of the resulting model,
interpolating between the usual Barrett-Crane model and a flat BF-type one.
Moreover, we define a further extension of the group field theory formalism in
which the coupling parameter enters as a new variable of the field, and the
action presents derivative terms that lead to modified classical equations of
motion. Finally, we discuss the issue of renormalisation of spin foam models,
and how the new coupled model can be of help regarding this.Comment: RevTeX, 18 pages, no figure
A quantum field theory of simplicial geometry and the emergence of spacetime
We present the case for a fundamentally discrete quantum spacetime and for
Group Field Theories as a candidate consistent description of it, briefly
reviewing the key properties of the GFT formalism. We then argue that the
outstanding problem of the emergence of a continuum spacetime and of General
Relativity from fundamentally discrete quantum structures should be tackled
from a condensed matter perspective and using purely QFT methods, adapted to
the GFT context. We outline the picture of continuum spacetime as a condensed
phase of a GFT and a research programme aimed at realizing this picture in
concrete terms.Comment: 10 pages, no figures; to appear in the Proceedings of the DICE 2006
Workshop (Piombino, Italy), uses IOP Conf style; v2: typos corrected, added
preprint number
Non-commutative flux representation for loop quantum gravity
The Hilbert space of loop quantum gravity is usually described in terms of
cylindrical functionals of the gauge connection, the electric fluxes acting as
non-commuting derivation operators. It has long been believed that this
non-commutativity prevents a dual flux (or triad) representation of loop
quantum gravity to exist. We show here, instead, that such a representation can
be explicitly defined, by means of a non-commutative Fourier transform defined
on the loop gravity state space. In this dual representation, flux operators
act by *-multiplication and holonomy operators act by translation. We describe
the gauge invariant dual states and discuss their geometrical meaning. Finally,
we apply the construction to the simpler case of a U(1) gauge group and compare
the resulting flux representation with the triad representation used in loop
quantum cosmology.Comment: 12 pages, matches published versio
Matter in Toy Dynamical Geometries
One of the objectives of theories describing quantum dynamical geometry is to
compute expectation values of geometrical observables. The results of such
computations can be affected by whether or not matter is taken into account. It
is thus important to understand to what extent and to what effect matter can
affect dynamical geometries. Using a simple model, it is shown that matter can
effectively mold a geometry into an isotropic configuration. Implications for
"atomistic" models of quantum geometry are briefly discussed.Comment: 8 pages, 1 figure, paper presented at DICE 200
Effective Hamiltonian Constraint from Group Field Theory
Spinfoam models provide a covariant formulation of the dynamics of loop
quantum gravity. They are non-perturbatively defined in the group field theory
(GFT) framework: the GFT partition function defines the sum of spinfoam
transition amplitudes over all possible (discretized) geometries and
topologies. The issue remains, however, of explicitly relating the specific
form of the group field theory action and the canonical Hamiltonian constraint.
Here, we suggest an avenue for addressing this issue. Our strategy is to expand
group field theories around non-trivial classical solutions and to interpret
the induced quadratic kinematical term as defining a Hamiltonian constraint on
the group field and thus on spin network wave functions. We apply our procedure
to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss
the relevance of understanding the spectrum of this Hamiltonian operator for
the renormalization of group field theories.Comment: 14 page
A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
Group Field Theories, a generalization of matrix models for 2d gravity,
represent a 2nd quantization of both loop quantum gravity and simplicial
quantum gravity. In this paper, we construct a new class of Group Field Theory
models, for any choice of spacetime dimension and signature, whose Feynman
amplitudes are given by path integrals for clearly identified discrete gravity
actions, in 1st order variables. In the 3-dimensional case, the corresponding
discrete action is that of 1st order Regge calculus for gravity (generalized to
include higher order corrections), while in higher dimensions, they correspond
to a discrete BF theory (again, generalized to higher order) with an imposed
orientation restriction on hinge volumes, similar to that characterizing
discrete gravity. The new models shed also light on the large distance or
semi-classical approximation of spin foam models. This new class of group field
theories may represent a concrete unifying framework for loop quantum gravity
and simplicial quantum gravity approaches.Comment: 48 pages, 4 figures, RevTeX, one reference adde
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