Related papers: Lecture Notes in Loop Quantum Gravity. LN2: Cauchy…
In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only "Log-Lipschitz" with respect to all the variables. This class of…
The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A…
By quantizing the background as well as the perturbations in a simple one fluid cosmological model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical…
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…
In this manuscript, we highlight a new phenomenon of complex algebraic singularity formation for solutions of a large class of genuinely nonlinear partial differential equations (PDEs). We start from a unique Cauchy datum, which is…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…
Spacetime singularities pose a long-standing puzzle in quantum gravity. Unlike Schwarzschild, a generic family of black holes gives rise to a Cauchy horizon on which, even in the Hartle-Hawking state, quantum observables such as $\langle…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity…
We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases…
We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
In the recent developments of regularization theory for inverse and ill-posed problems, a variational quasi-reversibility (QR) method has been designed to solve a class of time-reversed quasi-linear parabolic problems. Known as a PDE-based…
These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how…
Linear evolution equations are considered usually for the time variable being defined on an interval where typically initial conditions or time-periodicity of solutions are required to single out certain solutions. Here we would like to…
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…