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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…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
The problem of time emerging in the canonical quantization procedure of gravity signals a necessity to properly define a relational time parameter. Previous approaches, which are here briefly discussed, make use of the dependence of the…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
What if gravity is classical? If true, a consistent co-existence of classical gravity and quantum matter requires that gravity exhibit irreducible fluctuations. These fluctuations can mediate classical correlations, but not quantum…
We propose a step-by-step manual for the construction of alternative theories of gravity, perturbatively as well as nonperturbatively. The construction is guided by no more than two fundamental principles that we impose on the gravitational…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
We propose a "guide" towards quantisation of gravity based on quantum matter in a statistical mechanics context. On one hand, a statistical mechanics model naturally arises from the thermodynamic interpretation of horizons in Rindler space.…
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
Canonical coupling between classical and quantum systems cannot result in reversible equations, rather it leads to irreversible master equations. Coupling of quantized non-relativistic matter to gravity is illustrated by a simplistic…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…
A discursive, non-technical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the…
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…
The aim of this review is to provide a detailed account of the physical content emerging from this story of the canonical approach to Quantum Gravity. All the crucial steps in our presentation have a pedagogical character, providing the…
Simple cosmological models are used to show that gravitation can be quantized as an ordinary gauge system if the Hamilton-Jacobi equation for the model under consideration is separable. In this situation, a canonical transformation can be…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…