Related papers: Algebrodynamical Approach in Field Theory: Bisingu…
We review the algebraic field theory based completely on a nonlinear generalization of the CR complex analiticity conditions to the noncommutative algebra of biquaternions. Any biquaternionic field possesses natural twistor structure and,…
We consider a nonlinear generalization of Cauchy-Riemann eqs. to the algebra of biquaternions. From here we come to "universal generating equations" (1) which deal with 2-spinor and gauge fields and form the basis of some unified algebraic…
The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents…
A general method for the construction of solutions of the d'Alambertian and double d'Alambertian (harmonic and bi-harmonic) equations with local dependence of arbitrary functions upon two independent arguments is proposed. The connection…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field…
The purpose of this paper is to propose the implementation of some methods from algebraic geometry in the theory of gravitation, and more especially in the variational formalism. It has been assumed that the metric tensor depends on two…
We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the…
A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion…
The purpose of this paper is to explore, in a space of four-dimensions, the possible forms that second-order, bi-scalar-vector-tensor field equations derivable from a variational principle can assume. In order to restrict this enormous…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
This paper proposes a variational principle for the solutions of quantum field theories in which the ``trial functions'' are chosen from the algebra of asymptotic fields, and illustrates this variational principle in simple cases.
Recent experiments have demonstrated an interesting reaction on a gas-surface defined as epicatalysis. The non-equilibrium thermodynamic potentials were well described in a series of experiments. However the theoretical basis was not…
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…
We consider the four dimensional abelian topological BF theory with a planar boundary introduced following the Symanzik's method. We find the most general boundary conditions compatible with the fields equations broken by the boundary. The…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…