Related papers: Dirac equation for membranes
We obtain analytic solutions for the one-dimensional Dirac equation with the Morse potential as an infinite series of square integrable functions. These solutions are for all energies, the discrete as well as the continuous. The elements of…
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…
Tensor, matrix and quaternion 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…
The Dirac monopole problem is studied in details within the framework of infinite-dimensional representations of the rotation group, and a consistent pointlike monopole theory with an arbitrary magnetic charge is deduced.
We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the…
Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on…
Torsion in a 5D spacetime is considered. In this case gravitation is defined by the 5D metric and the torsion. It is conjectured that torsion is connected with a spinor field. In this case Dirac's equation becomes the nonlinear Heisenberg…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
The Dirac equation is generalized to $D+1$ space-time.The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd $D$ and even $D$ cases. The…
The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission…
There are two different methods to describe membrane (string) fluids, which use different field content. The relation between the methods is clarified by construction of combined method. Dirac membrane field appears naturally in new…
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In…
We consider the generalization of the Dirac equation where the mass term is an arbitrary matrix M. A general form of M, consistent with the mass shell constraint, is derived and proven to be equivalent to the original Dirac equation.
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints…
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…
A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_\mu dx^\mu$ is left invariant under the symmetry group…
Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are…
This paper investigates the Lorentz invariance of the multidimensional Dirac-Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct…