53 research outputs found
Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
We show how to properly gauge fix all the symmetries of the Ponzano-Regge
model for 3D quantum gravity. This amounts to do explicit finite computations
for transition amplitudes. We give the construction of the transition
amplitudes in the presence of interacting quantum spinning particles. We
introduce a notion of operators whose expectation value gives rise to either
gauge fixing, introduction of time, or insertion of particles, according to the
choice. We give the link between the spin foam quantization and the hamiltonian
quantization. We finally show the link between Ponzano-Regge model and the
quantization of Chern-Simons theory based on the double quantum group of SU(2)Comment: 48 pages, 15 figure
Ancient Maya Queenship: Generations of Crafting State Politics and Alliance Building from Kaanul to Waka\u27
Scalar-Tensor theories from Plebanski gravity
We study a modification of the Plebanski action, which generically
corresponds to a bi-metric theory of gravity, and identify a subclass which is
equivalent to the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories.
In this manner, scalar-tensor theories are displayed as constrained BF
theories. We find that in this subclass, there is no need to impose reality of
the Urbantke metrics, as also the theory with real bivectors is a scalar-tensor
theory with a real Lorentzian metric. Furthermore, while under the former
reality conditions instabilities can arise from a wrong sign of the scalar mode
kinetic term, we show that such problems do not appear if the bivectors are
required to be real. Finally, we discuss how matter can be coupled to these
theories. The phenomenology of scalar field dark matter arises naturally within
this framework.Comment: 21 page
Colored Group Field Theory
Group field theories are higher dimensional generalizations of matrix models.
Their Feynman graphs are fat and in addition to vertices, edges and faces, they
also contain higher dimensional cells, called bubbles. In this paper, we
propose a new, fermionic Group Field Theory, posessing a color symmetry, and
take the first steps in a systematic study of the topological properties of its
graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of
this theory are well defined and readily identified. We prove that this graphs
are combinatorial cellular complexes. We define and study the cellular homology
of this graphs. Furthermore we define a homotopy transformation appropriate to
this graphs. Finally, the amplitude of the Feynman graphs is shown to be
related to the fundamental group of the cellular complex
Before Kukulkán
This volume illuminates human lifeways in the northern Maya lowlands prior to the rise of Chichén Itzá. This period and area have been poorly understood on their own terms, obscured by scholarly focus on the central lowland Maya kingdoms. "Before Kukulkán" is anchored in three decades of interdisciplinary research at the Classic Maya capital of Yaxuná, located at a contentious crossroads of the northern Maya lowlands.
Using bioarchaeology, mortuary archaeology, and culturally sensitive mainstream archaeology, the authors create an in-depth regional understanding while also laying out broader ways of learning about the Maya past. Part 1 examines ancient lifeways among the Maya at Yaxuná, while part 2 explores different meanings of dying and cycling at the settlement and beyond: ancestral practices, royal entombment and desecration, and human sacrifice. The authors close with a discussion of the last years of occupation at Yaxuná and the role of Chichén Itzá in the abandonment of this urban center.
"Before Kukulkán" provides a cohesive synthesis of the evolving roles and collective identities of locals and foreigners at the settlement and their involvement in the region’s trajectory. Theoretically informed and contextualized discussions offer unique glimpses of everyday life and death in the socially fluid Maya city. These findings, in conjunction with other documented series of skeletal remains from this region, provide a nuanced picture of the social and biocultural dynamics that operated successfully for centuries before the arrival of the Itzá
Spin Foam Models of Yang-Mills Theory Coupled to Gravity
We construct a spin foam model of Yang-Mills theory coupled to gravity by
using a discretized path integral of the BF theory with polynomial interactions
and the Barret-Crane ansatz. In the Euclidian gravity case we obtain a vertex
amplitude which is determined by a vertex operator acting on a simple spin
network function. The Euclidian gravity results can be straightforwardly
extended to the Lorentzian case, so that we propose a Lorentzian spin foam
model of Yang-Mills theory coupled to gravity.Comment: 10 page
Discrete and continuum third quantization of Gravity
We give a brief introduction to matrix models and the group field theory
(GFT) formalism as realizations of the idea of a third quantization of gravity,
and present in some more detail the idea and basic features of a continuum
third quantization formalism in terms of a field theory on the space of
connections, building up on the results of loop quantum gravity that allow to
make the idea slightly more concrete. We explore to what extent one can
rigorously define such a field theory. Concrete examples are given for the
simple case of Riemannian GR in 3 spacetime dimensions. We discuss the relation
between GFT and this formal continuum third quantized gravity, and what it can
teach us about the continuum limit of GFTs.Comment: 21 pages, 5 eps figures; submitted as a contribution to the
proceedings of the conference "Quantum Field Theory and Gravity Conference
Regensburg 2010" (28 September - 1 October 2010, Regensburg/Bavaria); v2:
preprint number include
The complete 1/N expansion of colored tensor models in arbitrary dimension
In this paper we generalize the results of [1,2] and derive the full 1/N
expansion of colored tensor models in arbitrary dimensions. We detail the
expansion for the independent identically distributed model and the topological
Boulatov Ooguri model
Topological field theories in n-dimensional spacetimes and Cartan's equations
Action principles of the BF type for diffeomorphism invariant topological
field theories living in n-dimensional spacetime manifolds are presented. Their
construction is inspired by Cuesta and Montesinos' recent paper where Cartan's
first and second structure equations together with first and second Bianchi
identities are treated as the equations of motion for a field theory. In
opposition to that paper, the current approach involves also auxiliary fields
and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis
for the actions is detailedly carried out in the generic case and it is shown
that these action principles define topological field theories, as mentioned.
The current formalism is a generic framework to construct geometric theories
with local degrees of freedom by introducing additional constraints on the
various fields involved that destroy the topological character of the original
theory. The latter idea is implemented in two-dimensional spacetimes where
gravity coupled to matter fields is constructed out, which has indeed local
excitations.Comment: LaTeX file, no figure
Bubbles and jackets: new scaling bounds in topological group field theories
We use a reformulation of topological group field theories in 3 and 4
dimensions in terms of variables associated to vertices, in 3d, and edges, in
4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4
dimensions, we obtain a bubble bound proving the suppression of singular
topologies with respect to the first terms in the perturbative expansion (in
the cut-off). We also prove a new, stronger jacket bound than the one currently
available in the literature. We expect these results to be relevant for other
tensorial field theories of this type, as well as for group field theory models
for 4d quantum gravity.Comment: v2: Minor modifications to match published versio
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