Quantum constraints and dynamics:

Vadim Belov, II. Institute for Theoretical Physics, Hamburg: BF Gravity and the Poincare group

The significance of the “volume constraint” in the current Spin Foam models is highlighted, and indications are provided on its possible violation in models discretized over cell complexes more general than triangulations. Motivated by these findings, a possible interpretation and a tentative solution are proposed, by modifying the starting point and revisiting the action principle. The classical analysis of the resulting theory and of its gauge symmetries is performed combining both Lagrangian and Hamiltonian methods, which are shown to give equivalent results. A novel form of continuum linear simplicity constraints is proposed.

Christoph Charles, École Normale Supérieure de Lyon: Canonical quantization of the simplicity constraints: a 3d toy-model

The simplicity constraints are one of the points that must be implemented in order to understand Loop Quantum Gravity without the time-gauge. We explore the possibility of imposing such constraints at the quantum level in the context of canonical quantization. We suggest a new possibility to define such constraints using a natural extension of the Loop Quantum Gravity phase space to include the vielbein. We explore the idea in the context of discrete 3d quantum gravity which can act as a solvable toy-model for 4d quantum gravity. The construction requires the introduction of a dual support graph hinting towards a reduction to Regge geometries if applied in 4 dimensions. We discuss the generalization of our work to the continuum and to 4 dimensions.

Elena De Paoli, Università degli Studi Roma Tre: Sach's free data in real connection variables

We present various results for GR on a null foliation in the first order formalisms, with real connection variables. We begin with the non-trivial constraint structure, which includes tertiary constraints, and use the Newman-Penrose formalism to clarify its geometric meaning. We then present Sachs’s constraint-free data as the shear of an affine congruence, which is made geodesic and twist-free by the torsion-less condition; and show that the propagating Einstein’s equations, which are tertiary constraints in the formalism, have the role of preserving the metricity of the affine shear under retarded time evolution. Interestingly, what turns the propagating equations into constraints is the same mathematical identity that plays a role in Ashtekar’s construction of radiative data on scri in terms of asymptotic shear.

Pietro Dona, Centre de Physique Theorique, Marseille: Computing Lorentzian spin foam amplitudes: Overview

Explicit evaluations of spin foam transition amplitudes are hindered by their sheer complexity. This is particularly true for Lorentzian models, e.g. the EPRL model, due to the presence of non-compact integrals. An important step forward is possible thanks to the factorization property of SL(2,C) Clebsch-Gordan coefficients in terms of the more known and manageable SU(2) ones.
For the first time a number of analytical and numerical advances are possible, in particular a general estimation of scaling properties and divergences, as well as explicit numerical tests of the asymptotic formulas. The techniques developed can be applied also to generalized spin foams and drastic simplification happens in the extensions to imaginary Immirzi parameter.
In this talk I will give an overview of the factorization procedure and the results obtained for the EPRL model, mentioning some convenient and simplified models. Two associated talks will present more specific details.

Marco Fanizza, Scuola Normale Superiore di Pisa: Computing Lorentzian spin foam amplitudes: Semiclassics of the 15j symbol

We provide the first numerical confirmation of the asymptotic formula obtained by Barrett and collaborators for the SU(2) 15j symbol. The asymptotic is reached surprisingly fast, and the next-to-leading order has the same oscillating frequency. We also consider the case of the evaluation on Lorentzian boundary data, for which the amplitude is exponentially suppressed,  and comment on its role in the EPRL model. We show how Barrett’s analysis can be extended to polytopes, which is relevant for generalised spin foams such as the KKL model.

Marco Finocchiaro, Max Planck Institute for Gravitational Physics.: A new 4d Spinfoam model for euclidean Quantum Gravity. Analysis of the leading order radiative corrections.

In my talk I will present several recent results regarding a new class of 4d Spinfoam models (SF) for euclidean Quantum Gravity. They are obtained, as usual, by imposing at the quantum level the required geometricity constraints. Thus they depend on the prescriptions for defining and implementing the constraints as well as on additional choices in the construction (operator ordering, faces weights, etc).
In the first part of the talk I will review the above issues by comparing the resulting SF amplitudes for different models. I will then introduce a new 4d SF model defined in terms of non-commutative flux variables with Duflo quantization map, providing the corresponding formula of the effective edge amplitude encoding the constraints as restrictions on the spins. Its properties have been studied numerically and will be presented in the second part of the talk.
In the last part I will exploit the Group Field Theory (GFT) reformulation of the model to study the leading order radiative corrections to its n-point correlation functions (n<= 5). For this purpose the relevant (bulk) Feynman amplitudes have been evaluated via analytical and numerical methods focusing, in particular, on their large-j scaling behaviour. I will motivate the importance of this analysis, summarizing the main results and comparing them to those already known in the literature.

Igor Kanatchikov, School of Physics and Astronomy, University of St Andrews: Analysis of constraints and quantization within the De Donder-Weyl Hamiltonian formulation of GR

De Donder-Weyl theory in the calculus of variations can be viewed as a generalization of Hamiltonian formulation without the space-time decomposition. I show how the machinery of Poisson brackets, constraints and quantization is generalized to the vielbein GR within this approach and which type of quantum theory of gravity it leads to.

Klaus Liegener, Friedrich-Alexander University of Erlangen-Nurnberg: An effective Hamiltonian for Cosmology from full LQG dynamics

Starting with the scalar constraint of LQG as regularized by Thiemann we derive an effective Hamiltonian for Cosmology. This is achieved by picking the coherent state of a semiclassical isotropic spacetime and computing the expectation value of the Hamiltonian, which agrees with the dynamics of effective LQC at leading order and includes full-theory-corrections of order hbar.

Jan Sikorski, Faculty of Physics, University of Warsaw: Numerical take on evolution in LQG

I will present a numerical approach to dynamics in deparametrized LQG. We consider spin networks supported on a single fixed graph, and use a non graph changing version of the hamiltonian to numerically evaluate evolution of states.