468 research outputs found
Wilson loops, geometric operators and fermions in 3d group field theory
Group field theories whose Feynman diagrams describe 3d gravity with a
varying configuration of Wilson loop observables and 3d gravity with volume
observables at each vertex are defined. The volume observables are created by
the usual spin network grasping operators which require the introduction of
vector fields on the group. We then use this to define group field theories
that give a previously defined spin foam model for fermion fields coupled to
gravity, and the simpler quenched approximation, by using tensor fields on the
group. The group field theory naturally includes the sum over fermionic loops
at each order of the perturbation theory.Comment: 13 pages, many figures, uses psfra
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
Hidden Quantum Gravity in 3d Feynman diagrams
In this work we show that 3d Feynman amplitudes of standard QFT in flat and
homogeneous space can be naturally expressed as expectation values of a
specific topological spin foam model. The main interest of the paper is to set
up a framework which gives a background independent perspective on usual field
theories and can also be applied in higher dimensions. We also show that this
Feynman graph spin foam model, which encodes the geometry of flat space-time,
can be purely expressed in terms of algebraic data associated with the Poincare
group. This spin foam model turns out to be the spin foam quantization of a BF
theory based on the Poincare group, and as such is related to a quantization of
3d gravity in the limit where the Newton constant G_N goes to 0. We investigate
the 4d case in a companion paper where the strategy proposed here leads to
similar results.Comment: 35 pages, 4 figures, some comments adde
Quantum Gravity Momentum Representation and Maximum Invariant Energy
We use the idea of the symmetry between the spacetime coordinates x^\mu and
the energy-momentum p^\mu in quantum theory to construct a momentum space
quantum gravity geometry with a metric s_{\mu\nu} and a curvature
P^\lambda_{\mu\nu\rho}. For a closed maximally symmetric momentum space with a
constant 3-curvature, the volume of the p-space admits a cutoff with an
invariant maximum momentum a. A Wheeler-DeWitt-type wave equation is obtained
in the momentum space representation. The vacuum energy density and the
self-energy of a charged particle are shown to be finite, and modifications of
the electromagnetic radiation density and the entropy density of a system of
particles occur for high frequencies.Comment: 16 pages, LateX file, no figure
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
N=2 supersymmetric spin foams in three dimensions
We construct the spin foam model for N=2 supergravity in three dimensions.
Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has
representations which are not completely reducible. This complicates the
procedure when building a state sum. Fortunately, one can and should excise
these representations. We show that the restricted subset of representations
form a subcategory closed under tensor product. The resulting state-sum is once
again a topological invariant. Furthermore, within this framework one can
identify positively and negatively charged fermions propagating on the spin
foam. These results on osp(2|2) representations and intertwiners apply more
generally to spin network states for N=2 loop quantum supergravity (in 3+1
dimensions) where it allows to define a notion of BPS states.Comment: 12 page
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
Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with
massive particles and show that we recover in this limit Feynman graph
amplitudes (with Hadamard propagator) expressed as an abelian spin foam model.
We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be
resummed. This leads to the conclusion that the dynamics of quantum particles
coupled to quantum 3d gravity can be expressed in terms of an effective new non
commutative field theory which respects the principles of doubly special
relativity. We discuss the construction of Lorentzian spin foam models
including Feynman propagatorsComment: 46 pages, the wrong file was first submitte
Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
We show how the expectation values of geometrical quantities in 3d quantum
gravity can be explicitly computed using grasping rules. We compute the volume
of a labelled tetrahedron using the triple grasping. We show that the large
spin expansion of this value is dominated by the classical expression, and we
study the next to leading order quantum corrections.Comment: 18 pages, 1 figur
Group field theory formulation of 3d quantum gravity coupled to matter fields
We present a new group field theory describing 3d Riemannian quantum gravity
coupled to matter fields for any choice of spin and mass. The perturbative
expansion of the partition function produces fat graphs colored with SU(2)
algebraic data, from which one can reconstruct at once a 3-dimensional
simplicial complex representing spacetime and its geometry, like in the
Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs
for the matter fields. The model then assigns quantum amplitudes to these fat
graphs given by spin foam models for gravity coupled to interacting massive
spinning point particles, whose properties we discuss.Comment: RevTeX; 28 pages, 21 figure
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