Related papers: An Algebraic Foundation of Amended Dimensional Ana…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
On the verge of the centenary of dimensional analysis (DA), we present a generalisation of the theory and a methodology for the discovery of empirical laws from observational data. It is well known that DA: a) reduces the number of free…
Dimensional analysis is fundamental to the formulation and validation of physical laws, ensuring that equations are dimensionally homogeneous and scientifically meaningful. In this work, we use Lean 4 to formalize the mathematics of…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
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 describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and…
In this note a simple extension of the complex algebra to higher dimension is proposed. Using the postulated algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra…
First principles should predetermine physical geometry and dynamics both together. In the "algebrodynamics" they follow solely from the properties of the biquaternion algebra $\B$ and the analysis over $\B$. We briefly present the…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
We consider a simpler geometrical formulation of General Relativity based on non-metricity, known as Coincident General Relativity. We study the ADM formulation of the theory and perform a detailed Hamiltonian analysis. We explicitly show…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…