Related papers: Spectral Quadruples
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of…
The possibility of a complex 4-dimensional space-time manifold is suggested. This may imply the existence of a matter wave.
The new axiomatic system for the quantum field theory is proposed. The new axioms are the description of the distributions. For the finite series these distributions satisfy the linear Wightman axioms.
Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.
We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…
Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the…
We use the auxiliary fields and (excited-) de Sitter solutions to study the standard power spectrum of primordial fluctuations of a scalar field in the early universe. The auxiliary fields are the negative norm solutions of the field…
In a previous work, "pure data" is proposed as an axiomatic foundation for mathematics and computing, based on "finite sequence" as the foundational concept rather than based on logic or type. Within this framework, objects with…
Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the…
The symmetry between quarks and leptons suggests that neutrinos should have mass. As embodied in the grand unified theory SO(10) this yields masses that can only be detected by neutrino oscillations. Such oscillations could be very…
We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of…
I present arguments to the affect that the topological phase of string theory must be event-symmetric. This motivates a search for a universal string group for discrete strings in event-symmetric space-time which unifies space-time symmetry…
For nonautonomous linear differential equations with nonuniform hyperbolicity, we introduce a definition for nonuniform dichotomy spectrum, which can be seen as a generalization of Sacker-Sell spectrum. We prove a spectral theorem and use…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
We discuss the obstacles for defining a set of observable quantities analogous to an S-matrix which are needed to formulate string theory in an accelerating universe. We show that the quintessence models with the equations of state $-1 < w…
Spacetimes admitting a similarity group are considered. Amongst them, special attention is given to the 3-parameter ones. A classification of such spacetimes is given based on the Bianchi type of the similarity group $H_3$, and the general…
Using the reduced formulation of large-N Quantum Field Theories we study strings in space-time dimensions higher than one. Some preliminary results concerning the possible string susceptibilities and general properties of the model are…
Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}} \big(1 +\sum_{j=1}^{N-1} z^{n_j}\big)$ to be flat in almost…