The Stationary Dirac Equation as a Generalized Pauli Equation for Two Quasiparticles
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By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac’s theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a quantum dynamics of a single relativistic fermion, and its solution is reduced to solution of the generalized Pauli equation for two quasiparticles which move in the Euclidean space with their effective masses holding information about the Lorentzian symmetry of the four-dimensional space-time. We reveal the correspondence between the Dirac bispinor and Pauli spinor (two-component wave function), and show that all four components of the Dirac bispinor correspond to a fermion (or all of them correspond to its antiparticle). Mixing the particle and antiparticle states is prohibited. On this basis we discuss the paradoxical phenomena of Zitterbewegung and the Klein tunneling.
KeywordsDirac equation Klein tunneling Dirac sea Potential step
First of all I would like to thank Prof. I. L. Buchbinder for his useful critical remarks on the first version of the paper. I also thank Prof. V. G. Bagrov, Prof. V. A. Bordovitsyn and Prof. G. F. Karavaev for useful discussions on this subject. Finally, I want to express my deep gratitude to Reviewers for their helpful remarks and questions. This work was supported in part by the Programm of supporting the leading scientific schools of RF (Grant No 88.2014.2) for partial support of this work.
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