Related papers: Line geometry and electromagnetism IV: electromagn…
We propose a modification of standard linear electrodynamics in four dimensions, where effective non-trivial interactions of the electromagnetic field with itself and with matter fields induce Lorentz violating Chern-Simons terms. This…
Principal angles are used to define an angle bivector of subspaces, which fully describes their relative inclination. Its exponential is related to the Clifford geometric product of blades, gives rotors connecting subspaces via minimal…
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
We derive a necessary and sufficient condition for Poincar\'e Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the…
We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to…
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
We start from a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to $D=1+2$. The planar model resulting thereof is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar…
Similarity between the gravitoelectromagnetism and the electromagnetism is discussed. We show that the gravitomagnetic field (similar to the magnetic field) can be equivalent to the non-commutative effect of the momentum sector of the phase…
N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,R) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
We consider symmetry operations on the four-dimensional vector space that is spanned by the local versions of the Minkowski functionals (or fundamental measures): volume, surface, integral mean curvature, and Euler characteristic, of an…
We utilize an isomorphism between the character rings of the odd orthogonal group and the orthosymplectic supergroup to understand equivariant positivity properties of the type B quadric hypersurface ring. Our main result establishes a…
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation…
We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a…
We generalize the electromagnetic duality between a massless, canonical scalar field and a 2-form gauge field in 4-dimensional spacetime to scalar-tensor theories. We derive the action of 2-form gauge field that is dual to two kinds of…
In this work we develop a geometrical unification theory for gravity and the electro-weak model in a Kaluza-Klein approach; in particular, from the curvature dimensional reduction Einstein-Yang-Mills action is obtained. We consider two…
We revise and generalize the properties of the electric and the magnetic scalar potentials in spacetimes admitting a Killing vector field: Their constancy on the Killing horizons, uniqueness of solution for the electromagnetic test fields…
A new model of nonlinear electrodynamics named as \emph{"double-logarithmic"} is introduced and investigated. The theory carries one dimensionful parameter of the $\beta$ as Born-Infeld electrodynamics. It is shown that the dual symmetry…