Related papers: Towards general relativity through parametrized th…
Testing General Relativity (GR) is a key science goal of much of modern physics, and usually results in constraints that are either theory or context specific. We present an holistic framework that we dub `Parametrized Post-Newtonian…
The aim of this paper (Part III) is formulating GR as a scalar field theory. The basic structural elements of it are a generating function, a generalized density and a generalized temperature. One of the axioms of this theory is a…
In the first part of the present work, we focus on the theory of gravitoelectromagnetism (GEM), and we derive the full set of equations and constraints that the GEM scalar and vector potentials ought to satisfy. We discuss important aspects…
Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…
It has been proposed to study the theory resulting from setting the gravitational constant to zero in the first order formalism for general relativity. In this letter we investigate this theory in the presence of matter fields, establish…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
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 elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
In recent years it has been realized that in string/$M$ theories compactified to four dimensions which satisfy cosmological constraints, it is possible to make some generic predictions for particle physics and dark matter: a non-thermal…
Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…
These notes present an introduction to the method of geometric quantization. We discuss the main theorems in a style suitable for a theoretical physicist with an eye towards the physical motivation and the interpretation of the geometric…
Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
There exist several ways of constructing general relativity from `first principles': Einstein's original derivation, Lovelock's results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and…
The goal of this thesis is to develop the optimisation and generalisation theoretic foundations of learning in artificial neural networks. On optimisation, a new theoretical framework is proposed for deriving architecture-dependent…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This thesis studies general relativity (GR) using chiral formulations, which take advantage of the decomposition of the four-dimensional Lorentz group into self-dual and anti-self-dual sectors. Within this framework, GR can be expressed…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…