Related papers: A tensor form of the Dirac equation
The Dirac equation is reinterpreted as a constitutive equation for singularities in the electromagnetic vacuum, with the electron as a point singularity on a lightlike toroidal vortex. The diameter of the vortex is a Compton wavelength and…
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…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
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…
In this short note, we solve a Dirichlet problem for a fully nonlinear elliptic equation. The operator is introduced by S. Donaldson and it is relevant to the geometry of the space of volume forms.
The Lagrangian approach of Dirac is presented in a complete form. This suggests to identify the Schr\"{o}dinger equation as the Euler-Lagrange equation rather than the Hamiltonian operator equation.
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…
Approximate analytical solutions of the Dirac equation are obtained for the Yukawa potential plus a tensor interaction with any $\kappa$-value for the cases having the Dirac equation pseudospin and spin symmetry. The potential describing…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an…
We express the baryon magnetic moments in terms of the baryon tensor charges, considering the quarks as relativistic interacting objects. Once tensor charges get measured accurately, the formula for the baryon magnetic moment will serve to…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
One way of arriving at a quantum field theory of electrons and positrons is to take a classical theory of the Dirac field and then quantize. Starting with the standard classical field theory and quantizing in the most straightforward way…
A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
Dirac equation for the finite dipole potential is solved by the method of the join of the asymptotics. The formulas for the near continuum state energy term of a relativistic electron-dipole system are obtained analytically. Two cases are…
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 consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term…
The claim by Rohrlich that the Abraham-Lorentz-Dirac equation is not the correct equation for a classical point charge is shown to be incorrect and it is pointed out that the equation which he proposes is the equation {\underline{derived}}…
Tucker's Lemma is a combinatorial analog of the Borsuk-Ulam theorem and the case n=2 was proposed by Tucker in 1945. Numerous generalizations and applications of the Lemma have appeared since then. In 2006 Meunier proved the Lemma in its…