Related papers: A tensor interpretation of the 2D Dirac equation
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 suggest a tensor equation on Riemannian manifolds which can be considered as a generalization of the Dirac equation for the electron. The tetrad formalism is not used. Also we suggest a new form of the tensor Dirac equation with a…
Earlier we have shown that interacting electron-positron and electromagnetic fields can be considered as a certain microscopic distortion of pseudo-Euclidean properties of the Minkovsky 4-space-time. The known Dirac and Maxwell equations…
A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…
The article describes a new approach to obtaining the energy-momentum tensor of electromagnetic field in medium without the use of Maxwell's equations and Poynting theorem. The energy-momentum tensor has new qualities and consequences. Its…
We introduce a generalized tetrad which plays the role of a potential for torsion and makes torsion dynamic. Starting from the Einstein-Cartan action with torsion, we get two field equations, the Einstein equation and the torsion field…
Maxwell's equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which…
We prove the following theorem: the Dirac equation for an electron (invented by P.A.M.Dirac in 1928) can be written as a tensor equation. An equation is called a tensor equation if all values in it are tensors and all operations in it take…
Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor…
In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigatethe Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the…
We consider the Lagrangian density for a free Maxwell field, in which the electromagnetic field tensor minimally couples to the affine connection, in the Einstein-Cartan-Sciama-Kibble theory of gravity. We derive the formulae for the…
A unified field theory for the description of matter in a curved space is discussed. The description is based on a standard Lagrangianian formalism in a pseudo-Euclidian 4D continuum using a 3-index tensor as independent variables. The…
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 show that it is possible to formulate the classical Einstein-Maxwell-Dirac theory of spinors interacting with the gravitational and electromagnetic fields as the Einstein-Cartan-Kibble-Sciama theory with the Ricci scalar of the traceless…
According to Dirac's theory of the positron, an electromagnetic field tends to create pairs of particles which leads to a change of Maxwell's equations in the vacuum. These changes are calculated in the special case that no real electrons…
In December 1907, Minkowski expressed the Maxwell equations in the very beautiful and compact 4-dimensional form: lor f=-s, lor F^*=0. Here `lor', an abbreviation of Lorentz, represents the 4-dimensional differential operator. We study…
Considering a four dimensional parallelisable manifold, we develop a concept of Dirac-type tensor equations with wave functions that belong to left ideals of the set of nonhomogeneous complex valued differential forms.
Historically Gordon decomposition of Dirac current played an important role in the interpretation of Dirac equation. We revisit it to understand the correspondence between Maxwell-Dirac and Maxwell-Lorentz theories. Arguments are presented…
A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank two potential plus the dual of the gradient of a scalar field. Field equations for the theory are…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…