Classical model SDcl of the Dirac particle SD is constructed. SD is the dynamic system described by the Dirac equation. For investigation of SD and construction of SDcl one uses a new dynamic method: dynamic disquantization. This relativistic purely dynamic procedure does not use principles of quantum mechanics. The obtained classical analog SDcl is described by a system of ordinary differentia...

Formal and substantial analogies between the Boltzmann equation of classical statistical physics and the Dirac equation for relativistic quantum mechanics are discussed, with special emphasis on the Majorana representation of the Dirac equation, in which all matrices are real. It is shown that this property is instrumental in turning the Boltzmann-Dirac analogy into an efficient computational m...

This work clarifies the relation between Maxwell, Dirac and Majorana neutrino equations presenting an original way to derive the Dirac and neutrino equation from the chiral electrodynamics leading, perhaps, to novel conception in the mass generation by electromagnetic fields. In the present article, it is shown that Maxwell equations can be written in the same form as the two components Dirac a...

Classical model SDcl of the Dirac particle SD is constructed. SD is the dynamic system described by the Dirac equation. For investigation of SD and construction of SDcl one uses a new dynamic method: dynamic disquantization. This relativistic purely dynamic procedure does not use principles of quantum mechanics. The obtained classical analog SDcl is described by a system of ordinary differentia...

contains many of the features of the Dirac theory. The theory of spin-s free particles has been also developed by Proca [4], Kemmer [5] and Bargmann and Wigner [6]. All of these formalisms for spin-s free particles have many intrinsic contradictions and difficulties when an electromagnetic field interaction is introduced (see [7] and references therein). It should be noted that the mathematical...

Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the underlying quantum mechanics since the classical treatment is only an approximation. Quantum mechanical treatment of spin2 particle beam transport through o...

The Dirac equation is an important model in relativistic quantum mechanics. In the semi-classical regime ε≪1, even a spatially spectrally accurate time splitting method [6] requires the mesh size to be O(ε), which makes the direct simulation extremely expensive. In this paper, we present the Gaussian beam method for the Dirac equation. With the help of an eigenvalue decomposition, the Gaussian ...

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with qu...

The Weyl equation (massless Dirac equation) is studied in a family of metrics of the Gödel type. The field equation is solved exactly for one member of the family. PACS numbers 04.20q,04.20.Jb,04.40+c,98.80.k

The unitary quantum lattice gas (QLG) algorithm is a mesoscopic unitary perturbative representation that canmodel themean field Gross Pitaevskii equation for the evolution of the ground state wave function of Bose Einstein Condensates (BECs). The QLG considered here consists of an interleaved sequence of unitary collide-stream operators, with the collision operator being deduced from that for t...