2,557 research outputs found
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Spin foam models with finite groups
Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community we provide an introduction to some essential concepts in the loop quantum gravity, spin foam and group field theory approach and point out the many connections to lattice field theory and condensed matter systems
Social and Economic Impact of Solar Electricity at Schuchuli Village
Schuchuli, a small remote village on the Papago Indian Reservation in southwest Arizona, is 27 kilometers (17 miles) from the nearest available utility power. Its lack of conventional power is due to the prohibitive cost of supplying a small electrical load with a long-distance distribution line. Furthermore, alternate energy sources are expensive and place a burden on the resources of the villagers. On December 16, 1978, as part of a federally funded project, a solar cell power system was put into operation at Schuchuli. The system powers the village water pump, lighting for homes and other village buildings, family refrigerators and a communal washing machine and sewing machine
Quantum Gravity coupled to Matter via Noncommutative Geometry
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions
emerges in a semi-classical approximation from a construction which encodes the
kinematics of quantum gravity. The construction is a spectral triple over a
configuration space of connections. It involves an algebra of holonomy loops
represented as bounded operators on a separable Hilbert space and a Dirac type
operator. Semi-classical states, which involve an averaging over points at
which the product between loops is defined, are constructed and it is shown
that the Dirac Hamiltonian emerges as the expectation value of the Dirac type
operator on these states in a semi-classical approximation.Comment: 15 pages, 1 figur
Regge calculus from a new angle
In Regge calculus space time is usually approximated by a triangulation with
flat simplices. We present a formulation using simplices with constant
sectional curvature adjusted to the presence of a cosmological constant. As we
will show such a formulation allows to replace the length variables by 3d or 4d
dihedral angles as basic variables. Moreover we will introduce a first order
formulation, which in contrast to using flat simplices, does not require any
constraints. These considerations could be useful for the construction of
quantum gravity models with a cosmological constant.Comment: 8 page
On the Expansions in Spin Foam Cosmology
We discuss the expansions used in spin foam cosmology. We point out that
already at the one vertex level arbitrarily complicated amplitudes contribute,
and discuss the geometric asymptotics of the five simplest ones. We discuss
what type of consistency conditions would be required to control the expansion.
We show that the factorisation of the amplitude originally considered is best
interpreted in topological terms. We then consider the next higher term in the
graph expansion. We demonstrate the tension between the truncation to small
graphs and going to the homogeneous sector, and conclude that it is necessary
to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio
Towards computational insights into the large-scale structure of spin foams
Understanding the large-scale physics is crucial for the spin foam approach
to quantum gravity. We tackle this challenge from a statistical physics
perspective using simplified, yet feature-rich models. In particular, this
allows us to explicitly answer whether broken symmetries will be restored by
renormalization: We observe a weak phase transition in both Migdal-Kadanoff and
tensor network renormalization. In this work we give a concise presentation of
the concepts, results and promises of this new direction of research.Comment: 10 pages, 9 figures, to be published in proceedings of the Loops'11
Madrid international conference on quantum gravit
Towards computational insights into the large-scale structure of spin foams
Understanding the large-scale physics is crucial for the spin foam approach
to quantum gravity. We tackle this challenge from a statistical physics
perspective using simplified, yet feature-rich models. In particular, this
allows us to explicitly answer whether broken symmetries will be restored by
renormalization: We observe a weak phase transition in both Migdal-Kadanoff and
tensor network renormalization. In this work we give a concise presentation of
the concepts, results and promises of this new direction of research.Comment: 10 pages, 9 figures, to be published in proceedings of the Loops'11
Madrid international conference on quantum gravit
Towards computational insights into the large-scale structure of spin foams
Understanding the large-scale physics is crucial for the spin foam approach
to quantum gravity. We tackle this challenge from a statistical physics
perspective using simplified, yet feature-rich models. In particular, this
allows us to explicitly answer whether broken symmetries will be restored by
renormalization: We observe a weak phase transition in both Migdal-Kadanoff and
tensor network renormalization. In this work we give a concise presentation of
the concepts, results and promises of this new direction of research.Comment: 10 pages, 9 figures, to be published in proceedings of the Loops'11
Madrid international conference on quantum gravit
(Broken) Gauge Symmetries and Constraints in Regge Calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of
(quantum) gravity, in particular for Regge calculus. We find that for a
solution with curvature there do not exist exact gauge symmetries on the
discrete level. Furthermore we derive a canonical formulation that exactly
matches the dynamics and hence symmetries of the covariant picture. In this
canonical formulation broken symmetries lead to the replacements of constraints
by so--called pseudo constraints. These considerations should be taken into
account in attempts to connect spin foam models, based on the Regge action,
with canonical loop quantum gravity, which aims at implementing proper
constraints. We will argue that the long standing problem of finding a
consistent constraint algebra for discretized gravity theories is equivalent to
the problem of finding an action with exact diffeomorphism symmetries. Finally
we will analyze different limits in which the pseudo constraints might turn
into proper constraints. This could be helpful to infer alternative
discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure
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