Related papers: In quantum gravity, summing is refining
We explain how General Relativity with a cosmological constant arises as a broken symmetry phase of a BF theory. In particular we show how to treat de Sitter and anti-de Sitter cases simultaneously. This is then used to formulate a…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and…
The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently…
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own…
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first- and second-class quantum constraints, and (iii) a hard-core interpretation…
Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a…
$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann…
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
The first-order loop quantum gravity correction of the simplest, classical general-relativistic Friedmann Hamiltonian constraint, emerging from a holomorphic spinfoam cosmological model peaked on homogeneous, isotropic geometries, is…
Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
Semiclassical spin-coherent kinetic equations can be derived from quantum theory with many different approaches (Liouville equation based approaches, nonequilibrium Green's functions techniques, etc.). The collision integrals turn out to be…
Diagrammatic approaches to perturbation theory transformed the practicability of calculations in particle physics. In the case of extended theories of gravity, however, obtaining the relevant diagrammatic rules is non-trivial: we must…
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding…
The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…