Related papers: Shape Dynamics in 2+1 Dimensions
One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of an absolute space and time in which the physical objects are located and…
Shape dynamics is a theory first proposed by Julian Barbour which states that physics happen uniquely in the reduced configuration space of a theory. So far, studies in the area have focused on gravitational systems. Here we first…
This work presents a geometric formulation for transforming nonconservative mechanical Hamiltonian systems and introduces a new method for regularizing and linearizing central force dynamics -- in particular, Kepler and Manev dynamics --…
We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the…
The constraints of $BF$ topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of Topological Quantum Field Theories (TQFT's). By…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
A formalism is presented to construct a non-perturbative Grand Unified Theory when gravitational Planck-scale phenomena are included. The fundamental object on the Planck scale is the three-torus T^3 from which the known properties of…
It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…
In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…
The topology of orientable (2 + 1)d spacetimes can be captured by certain lumps of non-trivial topology called topological geons. They are the topological analogues of conventional solitons. We give a description of topological geons where…
Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic…
I present the first analytical study of gravitational collapse in a compact CMC foliation with $S^3$ spatial topology. The solutions I find, in this context, will be both solutions of Shape Dynamics and General Relativity. The aim is to…
3+1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we…
A closed 3-form $H \in \Omega^3_0(M)$ defines an extension of $\Gamma(TM)$ by $\Omega^2_0(M)$. This fact leads to the definition of the group of $H$-twisted Hamiltonian symmetries $\Ham(M, \JJ; H)$ as well as Hamiltonian action of Lie group…
We explore topological manipulations in one spatial dimension, which are defined for a system with a global symmetry and map the system to another one with a dual symmetry. In particular, we discuss fusion category symmetries enhanced by…
We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3+1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to…
The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…
In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional…
The restriction of space-time dimensions to "2+1" leads us to a novel quantum field theory which has the Chern-Simons term in its action. This term changes the nature of gauge interaction by giving a so-called topological mass to a gauge…
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and…