Related papers: Consistent discretizations for classical and quant…
In this article we give a systematic definition of the recently introduced spin foam models for four dimensional quantum gravity reviewing the main results on their semiclassical limit on fixed discretizations.
Spin foams provide path integrals for quantum gravity, which employ discretizations as regulator. To obtain regulator independent predictions, we must remove these fiducial structures in a suitable refinement limit. In this chapter we…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One…
Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leading order like a Stokes fluid with some explicit effective…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not…
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries…
The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are…
The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we…
We study an observable-based notion of equilibration and its application to realistic systems like spin qubits in quantum dots. On the basis of the so-called distinguishability, we analytically derive general equilibration bounds, which we…
In semiclassical gravity the back-reaction of the classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equations. A criterion for the validity of semiclassical gravity based on the…