Related papers: A note on the planar triangles in Minkowski spacet…
In this short paper I discuss how conformal geometric algebra models for euclidean and minkowski targetspaces determine the allowed quantum mechanical statespaces for free particles. I explicitly treat 2-dimensional euclidean space and…
We discuss the cosmology of a 3-brane embedded in a 5D bulk space-time with a cosmological constant when an intrinsic curvature Ricci scalar is included in the brane action. After deriving the `brane-Friedmann' equations for a Z_2…
The article is a tribute to Hermann Minkowski leading from his geometry of numbers to an attempt at using Finsler geometry for a break of Lorentz invariance.
The spacetime short-distance structure at the Planck scale is governed by the Planck length, usually interpreted as a three-dimensional Euclidian length. As such, it is not Lorentz invariant and clashes with Einstein's special relativity,…
As quotient spaces, Minkowski and de Sitter are fundamental, non-gravitational spacetimes for the construction of physical theories. When general relativity is constructed on a de Sitter spacetime, the usual Riemannian structure is replaced…
We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension $\geq 2$ and arbitrary co-dimension, provided they are initially close to a flat plane.
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and…
In this paper, we consider the idea of Bertrand curves for curves lying on surfaces in Minkowski 3-space. By considering the Darboux frame, we define these curves as Bertrand D-curves and give the characterizations for those curves. We also…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
In 1908, Minkowski put forward the idea that invariance under what we call today the Lorentz group, $GL(1,3, {\bf R})$, would be more meaningful in a four-dimensional space-time continuum. This suggestion implies that space and time are…
The article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and…
Cobalt nanoparticle-based ferrofluid in the presence of external magnetic field forms a self-assembled hyperbolic metamaterial. Wave equation describing propagation of extraordinary light inside the ferrofluid exhibits 2+1 dimensional…
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…
We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spaces equipped with a gauge. This is the first approach to…
In this paper we describe the moduli space of kinks in a class of systems of two coupled real scalar fields in (1+1) Minkowskian space-time. The main feature of the class is the spontaneous breaking of a discrete symmetry of (real)…
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a…
General relativity is applied to the strong interaction; the nexus between the two being arrived at by constructing a line element having the Yukawa form, which is used to describe geometrically the classical dynamics of a particle moving…
We re-examine the symmetry structure of massive momentum bispinors in four dimensional Minkowski spacetime and apply the result to the geometry of a two-qubit entanglement system. The geometry of entanglement is recovered by restricting the…