Related papers: Dirac and Maxwell equations in Split Octonions
The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant coordinate-free and the covariant coordinate forms. Also the…
We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced…
It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.
Maxwell's equation, Dirac's equation and the equation of gravito-electromagnetism are shown to be particular instances of the extended Maxwell system. The equations are discussed in the framework of the theory of evolutionary equations.…
The time dependent Dirac-Maxwell's Equations in presence of electric and magnetic sources are written in chiral media and the solutions for the classical problem are obtained in unique simple and consistent manner. The quaternion…
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…
We obtain the octonionic Bergman kernel for half space in the octonionic analysis setting by two different methods. As a consequence, we unify the kernel forms in both complex analysis and hyper-complex analysis.
The article is devoted to the issue of the polar form of octonions. This is a~continuation of the works initiated by Hahn and Snopek in their articles from 2011. The results presented in the article show errors made in previous…
Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black…
In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
We consider the representations of the optical Dirac equation, especially ones where the Hamiltonian is purely real-valued. This is equivalent, for Maxwell's equations, to the Majorana representation of the massless Dirac (Weyl) equation.…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
The Dirac equation with Lorentz violation involves additional coefficients and yields a fourth-order polynomial that must be solved to yield the dispersion relation. The conventional method of taking the determinant of $4\times 4$ matrices…
For an elliptic complex of first order differential operators on a smooth manifold, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to…
The slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative $ O(1) $ case to the non-commutative $ O(3) $…
Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed in unique, simple and consistent manner. It has been shown that this theory is extended consistently to time-harmonic…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery…
As is well-known, the real quaternion division algebra $ {\cal H}$ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra ${\cal O}$ can not be algebraically isomorphic to any matrix algebras…