Related papers: Point-Dimension Theory (Part I): The Point-Extende…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
Could one start from scratch, ignore relativity theory and quantum theory, create and expand our 3-D universe with no singularities, have the mathematical model predict correctly all of the cosmological parameters, provide the origins and…
In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries,…
Families of boxes in $\mathbb R^d$ are considered. In the paper an upper bound on the size of a minimum transversal in terms of the space dimension and the independence number of the given family was improved.
The nature of the change in perspective that accompanies the proposal of a unified physical theory deriving from the single dimension of time is elaborated. On expressing a temporal interval in a multi-dimensional form, via a direct…
The physics of a photonic structure is commonly described in terms of its apparent geometric dimensionality. On the other hand, with the concept of synthetic dimension, it is in fact possible to explore physics in a space with a…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
This paper presents an alternative quantum theory, the Theory of Discrete Extension, which avoids many of the conceptual problems of standard quantum mechanics. It is a deterministic, dynamic collapse theory with a well-defined primitive…
This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…
The ``N-Box Experiment'' is a much-discussed thought experiment in quantum mechanics. It is claimed by some authors that a single particle prepared in a superposition of N+1 box locations and which is subject to a final ``post-selection''…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
This article is based on papers discussing different aspects of extra dimensional environments. In addition to the results, we review some of the concepts on which models with large extra dimensions are based.
We prove three results on the dimension structure of complexity classes. 1. The Point-to-Set Principle, which has recently been used to prove several new theorems in fractal geometry, has resource-bounded instances. These instances…
The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…
Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and…
Changing the dimensionality of the space-time at the smallest and largest distances has manifold theoretical advantages. If the space is lower dimensional in the high energy regime, then there are no ultraviolet divergencies in field…
The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…
We propose an axiomatic approach to the concept of an intrinsic dimension of a dataset, based on a viewpoint of geometry of high-dimensional structures. Our first axiom postulates that high values of dimension be indicative of the presence…