Related papers: Approximate Canonical Quantization for Cosmologica…
The paper is the first of two parts of a work reviewing some approaches to the problem of time in quantum cosmology, which were put forward last decade, and which demonstrated their relation to the problems of reparametrization and gauge…
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…
In this article I introduce a distinction between two types of reparametrization invariant models and I argue that while both suffer from a problem of time at the time of applying canonical quantization methods to quantize them, its…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system…
Previous analysis about the deparametrization and path integral quantization of cosmological models are extended to models which do not admit an intrinsic time. The formal expression for the transition amplitude is written down for the Taub…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
The paper is the second part of the work devoted to the problem of time in quantum cosmology. Here we consider in detail two approaches within the scope of Feynman path integration scheme: The first, by Simeone and collaborators, is…
Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from…
The paper addresses the quantization of minisuperspace cosmological models, with application to the Taub Model. By desparametrizing the model with an extrinsic time, a formalism is developed in order to define a conserved Schr\"{o}dinger…
In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a…
A formalism for quantizing time reparametrization invariant dynamics is considered and applied to systems which contain an `almost ideal clock.' Previously, this formalism was successfully applied to the Bianchi models and, while it…
Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This…
The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on…
A midi-superspace model is a field theory obtained by symmetry reduction of a parent gravitational theory. Such models have proven useful for exploring the classical and quantum dynamics of the gravitational field. I present 3 recent…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…
Quantum cosmology in the presence of a fundamental minimal length is analyzed in the context of the flat isotropic and the Taub cosmological models. Such minimal scale comes out from a generalized uncertainty principle and the quantization…
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
We present a reformulation of the canonical quantization of gravity, as referred to the minisuperspace; the new approach is based on fixing a Gaussian (or synchronous) reference frame and then quantizing the system via the reconstruction of…