Related papers: Geometric Algebra Techniques for General Relativit…
This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…
As true as it is that a bricklayer needs a plumb line and a T-square, so it is that a physicist using general relativity needs how to draw geodesics and use fields of congruent vector frames of reference. While the first part of the…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
Computer algebra programs are presented for application in general relativity, in electrodynamics, and in gauge theories of gravity. The mathematical formalism used is the calculus of exterior differential forms, the computer algebra system…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general…
A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
We introduce the notion of rank of multivector in Clifford geometric algebras of arbitrary dimension without using the corresponding matrix representations and using only geometric algebra operations. We use the concepts of characteristic…
An attempt is made to describe the general-relativistic equations of motion for the Schwarzschild geometry in terms of the classical concepts of energy and angular momentum. Using the customary terms the geodesic equations can be viewed in…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat…
A null vector is an algebraic quantity with square equal to zero. I denote the universal algebra generated by taking all sums and products of null vectors over the real or complex numbers by N. The rules of addition and multiplication in N…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…