We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provide a new type of EinsteinDirac coupling. We establish a special method for con...

In the model of topological particles we have four types topologically stable dual Dirac monopoles with soft core and finite mass. We discuss steps how to get a equation for these particles. show free interacting case that arrive at in limit, where solitons approach singular monopoles.

A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy. Consider the Dirac equation of an electron

Dirac equation in (1+2) dimensions for quasi-particles in graphene and quantum field theory of their Coulomb interaction. Abstract There is evidence for existance of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's bril-luoin zone. Certain subtle points which are peculiar to od...

By analogy with the octonionic electromagnetic and gravitational interactions, the octonionic strong and weak interactions and their quantum interplays are discussed. In weak interaction, the study deduces some conclusions of field sources and intermediate particles, which are consistent with the Dirac equation, Yang-Mills equation, some new intermediate particles and three kinds of colors etc....

We analyse the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP) equation. Since the KDP–equation which describes spin-0 and spin-1 bosons is of Dirac-type, we examine some analogies and differences from the Dirac equation. The main difference to the Dirac equation is that the KDP equation contains redundant components. We will show that as a result certain interaction terms in the Ham...

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Will...

In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in R 3 by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using t...

We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green’s function in terms of the nonrelativistic Green’s function is first derived and then used to calculate the e...

This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The aim of the project was to study the Dirac equation in curved space time. To obtain the general relativistic Dirac equation we use the formulation of gravity as...