Related papers: Consistent discretizations as a road to quantum gr…
The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie…
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
We perform canonical quantization of General Relativity, as an effective quantum field theory below the Planck scale, within the BRST-invariant framework. We show that the promotion of constraints to dynamical equations of motion for…
Questioning the experimental basis of continuous descriptions of fundamental interactions we discuss classical gravity as an effective continuous first-order approximation of a discrete interaction. The sub-dominant contributions produce a…
Recently, a multigraviton theory on a simple closed circuit graph corresponding to the discretization of $S^1$ compactification of the Kaluza-Klein (KK) theory has been considered. In the present paper, we extend this theory to that on a…
A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are…
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 formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is…
We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein-Gordon and Chandrasekhar-Dirac equation are used to probe the classical timelike naked singularity. We…
One of the most important issues in quantum gravity is to identify its semi-classical regime. First the issue is to define for we mean by a semi-classical theory of quantum gravity, then we would like to use it to extract physical…
The construction of a continuum limit for the dynamics of loop quantum gravity is unavoidable to complete the theory. We explain that such a construction is equivalent to obtaining the continuum physical Hilbert space, which encodes the…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
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 discuss the relation between quantum curves (defined as solutions of equation $[P,Q]=\hbar$, where $P,Q$ are ordinary differential operators) and classical curves. We illustrate this relation for the case of quantum curve that…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
This is the current form of lecture notes on my approach to field quantization. I explain on a simple scalar-field model the physical motivation and show some preliminary applications (field produced by a pointlike charge, the…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…