Related papers: A concept of Dirac-type tensor equations
The goal of this work is to extend Dirac-type tensor equations to a curved space. We take four 1-forms (a tetrad) as a unique structure, which determines a geometry of space-time.
We suggest a so-called Dirac type tensor equation with nonabelian gauge symmetry on pseudo-Riemannian space. This equation reproduce some of the properties of spinor Dirac equation. A geometrical interpretation of results in terms of…
We present a so called Dirac-type tensor equation (DTTE). This equation is written in coordinateless form with the aid of differential operators $d$ and $\delta$. A wave function of DTTE belongs to a minimal left ideal of the algebra of…
In this article we develop energy methods for a large class of linear and nonlinear Dirac-type equations in two-dimensional Minkowski space. We will derive existence results for several Dirac-type equations originating in quantum field…
We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly…
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove…
We discuss a connection between the Dirac equation for an electron and the Dirac type tensor equation with ${\rm U}(1)$ gauge symmetry.
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…
On differential manifolds with spinor structure, it is possible to express the Euler and Pontryagin currents in terms of tensors that also appear as source in the Dirac equation. It is hence possible to tie concepts rooted in geometry and…
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…
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…
We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac…
One dimensional Dirac equation is analysed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the…
We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…
The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint…
Tensor and matrix formulations of Dirac-K\"ahler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection…
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…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…