Related papers: Shape dynamics and Mach's principles: Gravity from…
We derive an effective dynamics for scalar cosmological perturbations from quantum gravity, in the framework of group field theory (GFT) condensate cosmology. The emergent spacetime picture is obtained from the mean field hydrodynamic…
This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
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…
Do the spacetime manifolds which feature in our best scientific theories reflect anything metaphysically weighty in the world (e.g., any fundamental substances or relations)? Should we extend our notions of space and time beyond the…
We study the dynamics of countable groups on their respective spaces of quasimorphisms. For cohomologically non-trivial quasimorphisms we show that there are no invariant measures and classify stationary measures. Within the equivalence…
We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schr\"{o}dinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and…
We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local…
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…
We study the incorporation of gravity into the trace dynamics framework for classical matrix-valued fields, from which we have proposed that quantum field theory is the emergent thermodynamics, with state vector reduction arising from…
The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation plays the key role. In this paper we present an analysis of the…
Here we follow the mainstream of thinking about physical equivalence of different representations of a theory, regarded as the consequence of invariance of the laws of physics -- represented by an action principle and the derived motion…
In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology…
This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…
Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related…