Related papers: On precanonical quantization of gravity
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
A generalization of the recently formulated nonlinear quantization of a parameterized theory is presented in the context of quantum gravity. The parametric quantization of a Friedmann universe with a massless scalar field is then considered…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is available which allows one to address precise…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
In this article we present the quantization process for Schwarzschild space-time in the context of Teleparallel gravity. In order to achieve such a goal we use the Weyl formalism that establishes a well defined correspondence between…
The canonical ``loop'' formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the…
In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative…
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
In this review, we focus on whether a canonical quantization of general relativity can produce testable predictions for cosmology. In particular, we examine how this approach can be used to model the evolution of primordial perturbations.…
Standard approaches to quantum gravity start with a pre-spacetime structure and attempt, in accordance with Bohr's correspondence principle, to recover the pseudo-Riemannian manifold in the low energy limit. These approaches assume there is…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…
We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such…
A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears…
Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to…
These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…