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The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
A new family of coherent states for all dimensional loop quantum gravity are proposed, which is based on the generalized twisted geometry parametrization of the phase space of $SO(D+1)$ connection theory. We prove that this family of…
Quantum hypergraph states emerged in the literature as a generalization of graph states, and since then, considerable progress has been made toward implementing this class of genuine multipartite entangled states for quantum information and…
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems…
This article shows in detail the computations made for the poster presented at the Symposium "Frontiers of Fundamental Physics" in July 2014. As was shown in a previous publication, a quantum gravity formulation exists on the basis of…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here means a theory of quantum gravity arrived…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
We deepen the analysis of the cosmological acceleration produced by quantum gravity dynamics in the formalism of group field theory condensate cosmology, treated at the coarse-grained level via a phenomenological model, in the language of…
Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
Chamseddine and Mukhanov recently proposed a modified version of general relativity that implements the idea of a limiting curvature. In the spatially flat, homogeneous, and isotropic sector, their theory turns out to agree with the…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
In this work we propose a new general model of eternal cyclic Universe. We start from the assumption that quantum gravity corrections can be effectively accounted by the addition of higher order curvature terms in the Lagrangian density for…
We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge…