Canonical formalism for simplicial gravity

We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in particular.Comment: 4 pages, 5 figures, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

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

Conserved quantities in isotropic loop quantum cosmology

We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This quantity $Q$ relates the semi-classical limit of the wavefunction at large values of the spatial volume, but opposite triad orientations. Moreover, there is a similar quantity for generic difference equations of one parameter arising from a self-adjoint operator.Comment: 6 pages, to be published in Europhysics Letter

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

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

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