The stationary Dirac equation as a generalized Pauli equation for two quasiparticles

TL;DR

This paper demonstrates that the Dirac equation can be viewed as a generalized Pauli equation for two quasiparticles, clarifying its structure and implications for relativistic quantum dynamics.

Contribution

It shows that the Dirac equation is equivalent to a generalized Pauli equation for two quasiparticles, linking relativistic fermion dynamics to a two-particle quantum framework.

Findings

Dirac's theory is compatible with special relativity.

The Dirac bispinor corresponds to two quasiparticles with effective masses.

Particle-antiparticle mixing is prohibited in this framework.

Abstract

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 {\it quantum} dynamics of a {\it 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.