[en] The solutions of the Dirac equation with minimal and non-minimal coupling terms are investigated by transforming the relativistic equation into a Schroedinger-like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given. It is pointed out that techniques used in the analysis of quasi-exactly solvable potentials of non-relativistic quantum mechanics can be applied to relativistic problems as well. (author)

[en] Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity

No abstract available

[en] The Dirac equation in four dimension is studied describing fermions, both as 4 x 4 matrices and differential forms. It is discussed in both formalisms its properties under transformations of the group SU(4). (A.C.A.S.)

[en] Starting from the affinely parametrized supersymmetric Dirac particle model we derive a Grassmannian path integral expression for the propagator of the Dirac equation minimally coupled to an external electromagnetic field. We also obtain a purely 'bosonic' path integral representation of the propagator of the iterated minimally coupled Dirac equation. It appears that a Nicolai mapping exists, even in a formal sense, only in the case of a constant external field. (Author)

[en] With an arbitrary electromagnetic field, the Dirac equation is thought of as a space-time deformation, hence, it becomes possible to find explicit solutions without perturbation theory

[en] We prove, for small initial data, the existence and uniqueness of a global solution of a Dirac equation with cubic nonlinearity and zero mass

[en] The solution to the Poisson partial differential equation in mathematical physics is obtained by application of Dirac bra-ket vector analysis. (Author)

No abstract available

[en] The Laplacian nuclear force, investigated in Bulgaria last 30 Years, is in splendid agreement with the experiment. Thus it pretends to be the real basis of the theory of the nuclear forces. The basic points and results of nucleo-dynamics based on the new force are remembered. The paper shows how to use only the W-component of the nuclear Dirac equation and gives the basic principles of the used computer program in the case of np-scattering. A table of the obtained results is applied. (author)