Related papers: Quantum Gravity and Effective Topology
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
In this note, I review a recent approach to quantum gravity that "gravitizes" quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that…
We construct, in classical two-time physics, the necessary structure for the most general configuration space formulation of quantum mechanics containing gravity in d+2 dimensions. This structure is composed of a symmetric Riemannian metric…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum…
On the path towards quantum gravity, we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims…
Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a…
In this contribution, we discuss the asymptotic safety scenario for quantum gravity by evaluating the correlation functions of dynamical metric fluctuations. This is done with a functional renormalisation group approach that disentangles…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
The role of topology change in a fundamental theory of quantum gravity is still a matter of debate. However, when regarding string theory as two-dimensional quantum gravity, topological fluctuations are essential. Here we present a third…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
We formulate JT quantum gravity on a finite Lorentzian strip. Due to the spatial boundaries of the strip, it is possible to define left and right proper times. With respect to these times we compute non-perturbatively the quantum gravity…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. We…
One of the standard approaches of incorporating the quantum gravity (QG) effects into the semiclassical analysis is to adopt the notion of a quantum-corrected spacetime arising from the QG model. This procedure assumes that the expectation…
The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according on the sign of the cosmological constant. For $\Lambda>0$, saddle points can occur only for topologies with vanishing first Betti number and…
Geometrical properties of spacetime are difficult to study in nonperturbative approaches to quantum gravity like Causal Dynamical Triangulations (CDT), where one uses simplicial manifolds to define the gravitational path integral, instead…