Related papers: Algebrodynamical Approach in Field Theory: Bisingu…
We use the correspondence between the $f(R)$ theory and an Einstein-scalar field system to study late-time dynamics of solutions of $f(R)$ theory. We discuss how reasonable assumptions on the potential of the scalar field lead to…
In this note we develop a coalgebraic approach to the study of solutions of linear difference equations over modules and rings. Some known results about linearly recursive sequences over base fields are generalized to linearly (bi)recursive…
The thesis developed by Cornelius Lanczos in his doctoral dissertation is that electrodynamics is a pure field theory which is hyperanalytic over the algebra of biquaternions. In this theory Maxwell's homogeneous equations correspond to a…
The problem of extending derivations of a field $F$ to an $F-$algebra $B$ is widely studied in commutative algebra and non-commutative ring theory. For example, every derivation of $F$ extends to $B$ if $B$ is a separable algebraic…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
Field transformations for the quantum effective action lead to different pictures of a given physical situation, as describing a given evolution of the universe by different geometries. Field transformations for functional flow equations…
Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic…
A variational phase space is constructed for a system of fields on Euclidean space with periodic boundary conditions. An extended action functional is defined such that the Euler-Lagrange equations generate a symplectic flow on the…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
In this paper we associate an invariant to a biquaternion algebra $B$ over a field $K$ with a subfield $F$ such that $K/F$ is a quadratic separable extension and $\operatorname{char}(F)=2$. We show that this invariant is trivial exactly…
The main purpose of this contribution is to determine physical and geometrical characterizations of whole classes of stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional…
We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged…
From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…