Related papers: Complex geometry and pre-metric electromagnetism
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular…
In this manuscript we provide a fully geometric formulation for the induced electromagnetic fields and their corresponding constitutive relations in moving media. To this end, we present the reader with a brief geometric summary to show how…
We present a scheme of biquaternionic algebrodymamics based on a nonlinear generalization of the Cauchy-Riemann holomorphy conditions considered therein as fundamental field equations. The automorphism group SO(3,C) of the biquaternion…
We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii.)…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
We establish duality between real forms of the quantum deformation of the 4-dimensional orthogonal group studied by Fioresi et al. and the classification work made by Borowiec et al.. Classically these real forms are the isometry groups of…
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…
It is shown that every regular electromagnetic field in vacuum identically satisfy Maxwell equations in a new manifold where the roles of space and time have been exchanged. The new metric is Lorentzian, depends on the particular solution…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler…
In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field F is decomposed into the observer dependent sum of a relative vector E and a relative bivector e_5 B by making a space-time split, which depends on the…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
We start by formulating geometrically the Newton's law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. In fact, we use this scheme for further generalisation devoted to a constrained…
We construct the general action for Abelian vector multiplets in rigid 4-dimensional Euclidean (instead of Minkowskian) N=2 supersymmetry, i.e., over space-times with a positive definite instead of a Lorentzian metric. The target manifolds…
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor {\mu} \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients…
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…