1,302 research outputs found
Quantum Gravity as a Deformed Topological Quantum Field Theory
It is known that the Einstein-Hilbert action with a positive cosmological
constant can be represented as a perturbation of the SO(4,1) BF theory by a
symmetry-breaking term quadratic in the B field. Introducing fermionic matter
generates additional terms in the action which are polynomial in the tetrads
and the spin connection. We describe how to construct the generating functional
in the spin foam formalism for a generic BF theory when the sources for the B
and the gauge field are present. This functional can be used to obtain a path
integral for General Relativity with matter as a perturbative series whose the
lowest order term is a path integral for a topological gravity coupled to
matter.Comment: 7 pages, talk presented at the QG05 conference, 12-16 September 2005,
Cala Gonone, Ital
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
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
From twistors to twisted geometries
In a previous paper we showed that the phase space of loop quantum gravity on
a fixed graph can be parametrized in terms of twisted geometries, quantities
describing the intrinsic and extrinsic discrete geometry of a cellular
decomposition dual to the graph. Here we unravel the origin of the phase space
from a geometric interpretation of twistors.Comment: 9 page
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