Related papers: On the mathematical origin of quantum space-time
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
A class of homogeneous isotropic space-time models including pseudo-Euclidean space as a special case is considered. Such a model is chosen, where the particle motion is described in the most adequate way. It means that the world tubes of…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…
We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…
I extend the three-dimensional q-deformed Euclidean space by a time element and discuss the algebraic structure of this quantum space together with its differential calculi. Using the star-product formalism, I will give basic operations of…
Invariant integrals of functions and forms over $q$ - deformed Euclidean space and spheres in $N$ dimensions are defined and shown to be positive definite, compatible with the star - structure and to satisfy a cyclic property involving the…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…
It is shown that nearly-flat 3+1D spacetime emerging from a dual quantum field theory in 2+1D displays quantum fluctuations from classical Euclidean geometry on macroscopic scales. A covariant holographic mapping is assumed, where plane…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
We present the class of deformations of simple Euclidean superalgebra, which describe the supersymmetrization of some Lie algebraic noncommutativity of D=4 Euclidean space-time. The presented deformations are generated by the supertwists.…
We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
The description of space-time in a quantum theoretical framework must be considered as a fundamental problem in physics. Most attempts start with an already given classical space-time - then the quantization is done. In contrast to this the…
We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\rn_q^N\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \cite{fioeu}, which turn out to be rather simple "lattice-regularized" versions of the…
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,…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
Erd\H{o}s space $\mathfrak{E}$ and complete Erd\H{o}s space $\mathfrak{E}_c$ have been previously shown to have topological characterizations. In this paper, we provide a topological characterization of the topological space…