Related papers: Quantum Geometry I : Basics of Loop Quantum Gravit…
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to…
First, we review the $C^\ast$-algebraic foundations of loop quantization, in particular, the construction of quantum configuration spaces and the implementation of symmetries. Then, we apply these results to loop quantum gravity, focusing…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
We present a pedagogical introduction to the notions underlying the connection formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General…
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
The quantum geometry arising in Loop Quantum Gravity has been known to semi-classically lead to generalizations of length-geometries. There have been several attempts to interpret these so called twisted geometries and understand their role…
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…