Related papers: Space-time dynamics from algebra representations
The aim of this contribution is twofold. First, we show that when two (or more) different quantum groups share the same noncommutative spacetime, such an 'ambiguity' can be resolved by considering together their corresponding noncommutative…
We argue that special and general theories of relativity implicitly assume spacetime events correspond to quantum measurement outcomes. This leads to a change in how one should view the equivalence of spacetime and gravity. We describe a…
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are…
The relativistic theory of unconstrained $p$-dimensional membranes ($p$-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in…
This research notes is intended to provide a quick introduction to the subject. We expose a K-theoretic approach to study group C*-algebras: started in the elementary part, with one example of description of the structure of C*-algebras of…
Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…
The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques…
Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The spacetime consists of one timelike dimension and two maximally symmetric subspaces, filled with…
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…
Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…
In this second part about dynamics of atomic system we revisit the logic application of $SU(2)$ dynamics. We reiterate that solution of quantum dynamics systems can be represented geometrically. Such geometric representations of solutions…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…
We discuss a model of a conformal p-brane interacting with the world volume metric and connection. The purpose of the model is to suggest a mechanism by which gravity coupled to p-branes leads to the formation of structure rather than…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological…
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…