1,872 research outputs found
The Holst Spin Foam Model via Cubulations
Spin foam models are an attempt for a covariant, or path integral formulation
of canonical loop quantum gravity. The construction of such models usually rely
on the Plebanski formulation of general relativity as a constrained BF theory
and is based on the discretization of the action on a simplicial triangulation,
which may be viewed as an ultraviolet regulator. The triangulation dependence
can be removed by means of group field theory techniques, which allows one to
sum over all triangulations. The main tasks for these models are the correct
quantum implementation of the Plebanski constraints, the existence of a
semiclassical sector implementing additional "Regge-like" constraints arising
from simplicial triangulations, and the definition of the physical inner
product of loop quantum gravity via group field theory. Here we propose a new
approach to tackle these issues stemming directly from the Holst action for
general relativity, which is also a proper starting point for canonical loop
quantum gravity. The discretization is performed by means of a "cubulation" of
the manifold rather than a triangulation. We give a direct interpretation of
the resulting spin foam model as a generating functional for the n-point
functions on the physical Hilbert space at finite regulator. This paper focuses
on ideas and tasks to be performed before the model can be taken seriously.
However, our analysis reveals some interesting features of this model: first,
the structure of its amplitudes differs from the standard spin foam models.
Second, the tetrad n-point functions admit a "Wick-like" structure. Third, the
restriction to simple representations does not automatically occur -- unless
one makes use of the time gauge, just as in the classical theory.Comment: 25 pages, 1 figure; v3: published version. arXiv admin note:
substantial text overlap with arXiv:0911.213
Learning about Quantum Gravity with a Couple of Nodes
Loop Quantum Gravity provides a natural truncation of the infinite degrees of
freedom of gravity, obtained by studying the theory on a given finite graph. We
review this procedure and we present the construction of the canonical theory
on a simple graph, formed by only two nodes. We review the U(N) framework,
which provides a powerful tool for the canonical study of this model, and a
formulation of the system based on spinors. We consider also the covariant
theory, which permits to derive the model from a more complex formulation,
paying special attention to the cosmological interpretation of the theory
Quantum Spin Dynamics VIII. The Master Constraint
Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG)
was launched which replaces the infinite number of Hamiltonian constraints by a
single Master constraint. The MCP is designed to overcome the complications
associated with the non -- Lie -- algebra structure of the Dirac algebra of
Hamiltonian constraints and was successfully tested in various field theory
models. For the case of 3+1 gravity itself, so far only a positive quadratic
form for the Master Constraint Operator was derived. In this paper we close
this gap and prove that the quadratic form is closable and thus stems from a
unique self -- adjoint Master Constraint Operator. The proof rests on a simple
feature of the general pattern according to which Hamiltonian constraints in
LQG are constructed and thus extends to arbitrary matter coupling and holds for
any metric signature. With this result the existence of a physical Hilbert
space for LQG is established by standard spectral analysis.Comment: 19p, no figure
Improving the Asymmetric TSP by Considering Graph Structure
Recent works on cost based relaxations have improved Constraint Programming
(CP) models for the Traveling Salesman Problem (TSP). We provide a short survey
over solving asymmetric TSP with CP. Then, we suggest new implied propagators
based on general graph properties. We experimentally show that such implied
propagators bring robustness to pathological instances and highlight the fact
that graph structure can significantly improve search heuristics behavior.
Finally, we show that our approach outperforms current state of the art
results.Comment: Technical repor
An extension of Canonical Tensor Model
Tensor models are generalizations of matrix models, and are studied as
discrete models of quantum gravity for arbitrary dimensions. Among them, the
canonical tensor model (CTM for short) is a rank-three tensor model formulated
as a totally constrained system with a number of first-class constraints, which
have a similar algebraic structure as the constraints of the ADM formalism of
general relativity. In this paper, we formulate a super-extension of CTM as an
attempt to incorporate fermionic degrees of freedom. The kinematical symmetry
group is extended from to , and the constraints are
constructed so that they form a first-class constraint super-Poisson algebra.
This is a straightforward super-extension, and the constraints and their
algebraic structure are formally unchanged from the purely bosonic case, except
for the additional signs associated to the order of the fermionic indices and
dynamical variables. However, this extension of CTM leads to the existence of
negative norm states in the quantized case, and requires some future
improvements as quantum gravity with fermions. On the other hand, since this is
a straightforward super-extension, various results obtained so far for the
purely bosonic case are expected to have parallels also in the super-extended
case, such as the exact physical wave functions and the connection to the dual
statistical systems, i.e. randomly connected tensor networks.Comment: 27pages, 27 figure
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