Related papers: 'Shape Dynamics': Foundations Reassessed
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate…
We present a novel Finite Volume (FV) scheme on unstructured polygonal meshes that is provably compliant with the Second Law of Thermodynamics and the Geometric Conservation Law (GCL) at the same time. The governing equations are provided…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
The paper discusses the possible implications of the relational framework of Pure Shape Dynamics for the metaphysics of time. The starting point of the analysis is an interpretation of shapes in ontic structural realist terms, which gives…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…
This series of works revisits the geometry, dynamics, and covariant phase space of spherically symmetric spacetimes with the aim of exploring the thermodynamics of spacetime from their dynamical properties. In this first paper, we examine…
Self-assembly kinetics is usually described by approaches which assume that the shape of the aggregates has a definite form (e.g., spherical, cylindrical, cubic, etc), however that is unlikely to be the case in many finite-sized…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field…
This thesis embarks on a comprehensive investigation of modified gravity theories and their implications on the properties of compact objects. Our primary objective is to shed light on the fundamental nature of gravity by exploring…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
Four-dimensional CDT (causal dynamical triangulations) is a lattice theory of geometries which one might use in an attempt to define quantum gravity non-perturbatively, following the standard procedures of lattice field theory. Being a…
In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…
The conception of the conformal phase transition (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is discussed.