Related papers: Algebrodynamical Approach in Field Theory: Bisingu…
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein…
In this paper, we review two related aspects of field theory: the modeling of the fields by means of exterior algebra and calculus, and the derivation of the field dynamics, i.e., the Euler-Lagrange equations, by means of the stationary…
The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four dimensional spacetime. The presence of a boundary breaks the Ward identities which describe the gauge symmetries of the theory, and, using standard…
The Maxwell equations for chiral media are treated with the aid of quaternionic analysis methods. Besides the possibility of simplification of the form of such basic facts like the Stratton-Chu formulas we obtain a criterion for the…
We present a new formulation of self-dual nonlinear electrodynamics in which interactions are determined by an auxiliary-field potential, with causality ensuring a unique solution to the auxiliary-field equation. The long-standing problem…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
The algebraic structure of Thermo Field Dynamics lies in the $q$-deformation of the algebra of creation and annihilation operators. Doubling of the degrees of freedom, tilde-conjugation rules, and Bogoliubov transformation for bosons and…
We update and detail the formulation of the duality-invariant systems of N interacting abelian gauge fields with N auxiliary bispinor fields added. In this setting, the self-duality amounts to U(N) invariance of the nonlinear interaction of…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…
The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in…
A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and a condition is additionally imposed on the latter that ensures the classical character…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…