Related papers: Space-time dynamics from algebra representations
Certain well-known spacetimes of general relativity (GR) are generated from the collision of suitable null-sources coupled with gravitational waves. This is a classical process underlying the full nonlinearity of GR that may be considered…
We discuss a 4D noncommutative space-time as suggested by the version of quantum (deformed) relativity which provides a classical geometry picture as an `AdS_5'. The 4D noncommutative space-time is more like a part of a phase space…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…
We begin from the generalised eight-dimensional Minkowski spacetime structure, previously developed in Clifford geometric algebra $ C\ell(\Re^3) $. We propose that this is the correct algebraic representation for physical three-dimensional…
Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…
We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective…
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is…
We study modified gravity theory known as Regge-Teitelboim approach, in which the gravity is represented by dynamics of a surface isometrically embedded in a flat bulk. We obtain some particular solutions of Regge-Teitelboim equations…
This paper explores the application of geometric algebra to Galilean spacetime and its physical implications. We introduce the Galilean Spacetime Algebra (GSTA), a five-dimensional conformal geometric algebra (CGA) generated by a specific…
In the last decades the logico-algebraic approach to quantum mechanics turned to be a successful tool to render the quantum mechanical formalism on a steady operationalistic background. The algebraic approach to general relativity first…
We suggest a mechanism for the emergence of classical dynamical spacetime from an underlying quantum gravitational system. This is an example of a more general process, which we name micro-equilibration, and which can be thought of as local…
In this paper we introduce a definition of time that emerges in terms of the geometry of the configuration space of a dynamical system. We illustrate this, using the Hamilton-Jacobi equation, in various examples: particle mechanics on a…
A host algebra of a topological group G is a C^*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite…
We characterize the topology of the Glimm space of a separable C*-algebra and extend the main result of [6] to non-unital AF C*-algebras.
In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial…
A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter…
I show how the isomorphism between the Lie groups of types $B_2$ and $C_2$ leads to a faithful action of the Clifford algebra $\mathcal C\ell(3,2)$ on the phase space of 2-dimensional dynamics, and hence to a mapping from Dirac spinors…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
The fundamental physical object of the Global Time Theory is a three-dimensional curved space dynamically developing in global time. The equations of its dynamics are derived from the Lagrangian, and the Hamiltonian of ravitation turns out…