577 research outputs found
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
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
Canonical analysis of the BCEA topological matter model coupled to gravitation in (2+1) dimensions
We consider a topological field theory derived from the Chern - Simons action
in (2+1) dimensions with the I(ISO(2,1)) group,and we investigate in detail the
canonical structure of this theory.Originally developed as a topological theory
of Einstein gravity minimally coupled to topological matter fields in (2+1)
dimensions, it admits a BTZ black-hole solutions, and can be generalized to
arbitrary dimensions.In this paper, we further study the canonical structure of
the theory in (2+1) dimensions, by identifying all the distinct gauge
equivalence classes of solutions as they result from holonomy considerations.
The equivalence classes are discussed in detail, and examples of solutions
representative of each class are constructed or identified.Comment: 17 pages, no figure
Spin foam model from canonical quantization
We suggest a modification of the Barrett-Crane spin foam model of
4-dimensional Lorentzian general relativity motivated by the canonical
quantization. The starting point is Lorentz covariant loop quantum gravity. Its
kinematical Hilbert space is found as a space of the so-called projected spin
networks. These spin networks are identified with the boundary states of a spin
foam model and provide a generalization of the unique Barrette-Crane
intertwiner. We propose a way to modify the Barrett-Crane quantization
procedure to arrive at this generalization: the B field (bi-vectors) should be
promoted not to generators of the gauge algebra, but to their certain
projection. The modification is also justified by the canonical analysis of
Plebanski formulation. Finally, we compare our construction with other
proposals to modify the Barret-Crane model.Comment: 26 pages; presentation improved, important changes concerning the
closure constraint and the vertex amplitude; minor correctio
Bubble divergences from cellular cohomology
We consider a class of lattice topological field theories, among which are
the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d
quantum gravity and discrete BF theory, whose dynamical variables are flat
discrete connections with compact structure group on a cell 2-complex. In these
models, it is known that the path integral measure is ill-defined in general,
because of a phenomenon called `bubble divergences'. A common expectation is
that the degree of these divergences is given by the number of `bubbles' of the
2-complex. In this note, we show that this expectation, although not realistic
in general, is met in some special cases: when the 2-complex is simply
connected, or when the structure group is Abelian -- in both cases, the
divergence degree is given by the second Betti number of the 2-complex.Comment: 5 page
Quantum geometry from phase space reduction
In this work we give an explicit isomorphism between the usual spin network
basis and the direct quantization of the reduced phase space of tetrahedra. The
main outcome is a formula that describes the space of SU(2) invariant states by
an integral over coherent states satisfying the closure constraint exactly, or
equivalently, as an integral over the space of classical tetrahedra. This
provides an explicit realization of theorems by Guillemin--Sternberg and Hall
that describe the commutation of quantization and reduction. In the final part
of the paper, we use our result to express the FK spin foam model as an
integral over classical tetrahedra and the asymptotics of the vertex amplitude
is determined.Comment: 33 pages, 1 figur
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
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
We show how Feynman amplitudes of standard QFT on flat and homogeneous space
can naturally be recast as the evaluation of observables for a specific spin
foam model, which provides dynamics for the background geometry. We identify
the symmetries of this Feynman graph spin foam model and give the gauge-fixing
prescriptions. We also show that the gauge-fixed partition function is
invariant under Pachner moves of the triangulation, and thus defines an
invariant of four-dimensional manifolds. Finally, we investigate the algebraic
structure of the model, and discuss its relation with a quantization of 4d
gravity in the limit where the Newton constant goes to zero.Comment: 28 pages (RevTeX4), 7 figures, references adde
Scalar Asymptotic Charges and Dual Large Gauge Transformations
In recent years soft factorization theorems in scattering amplitudes have
been reinterpreted as conservation laws of asymptotic charges. In gauge,
gravity, and higher spin theories the asymptotic charges can be understood as
canonical generators of large gauge symmetries. Such a symmetry interpretation
has been so far missing for scalar soft theorems. We remedy this situation by
treating the massless scalar field in terms of a dual two-form gauge field. We
show that the asymptotic charges associated to the scalar soft theorem can be
understood as generators of large gauge transformations of the dual two-form
field.
The dual picture introduces two new puzzles: the charges have very unexpected
Poisson brackets with the fields, and the monopole term does not always have a
dual gauge transformation interpretation. We find analogs of these two
properties in the Kramers-Wannier duality on a finite lattice, indicating that
the free scalar theory has new edge modes at infinity that canonically commute
with all the bulk degrees of freedom.Comment: 16 pages, 2 figure
Holomorphic Simplicity Constraints for 4d Spinfoam Models
Within the framework of spinfoam models, we revisit the simplicity
constraints reducing topological BF theory to 4d Riemannian gravity. We use the
reformulation of SU(2) intertwiners and spin networks in term of spinors, which
has come out from both the recently developed U(N) framework for SU(2)
intertwiners and the twisted geometry approach to spin networks and spinfoam
boundary states. Using these tools, we are able to perform a
holomorphic/anti-holomorphic splitting of the simplicity constraints and define
a new set of holomorphic simplicity constraints, which are equivalent to the
standard ones at the classical level and which can be imposed strongly on
intertwiners at the quantum level. We then show how to solve these new
holomorphic simplicity constraints using coherent intertwiner states. We
further define the corresponding coherent spin network functionals and
introduce a new spinfoam model for 4d Riemannian gravity based on these
holomorphic simplicity constraints and whose amplitudes are defined from the
evaluation of the new coherent spin networks.Comment: 27 page
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