Only in the standard representation the Dirac theory is a quantum theory of a single fermion

It is shown that the relativistic quantum mechanics of a single fermion can be developed only on the basis of the standard representation of the Dirac bispinor. As in the nonrelativistic quantum mechanics, the arbitrariness in defining the bispinor, as a four-component wave function, is restricted by its multiplication by an arbitrary phase factor. We reveal the role of the large and small components of the bispinor, establish their link in the nonrelativistic limit with the Pauli spinor, as well as explain the role of states with negative energies. The Klein tunneling is treated here as a physical phenomenon analogous to the propagation of the electromagnetic wave in a medium with negative dielectric permittivity and permeability. For the case of localized stationary states we define the effective one-particle operators which act in the space of the large component but contain the contributions of both components. The effective operator of energy is presented in a compact analytical form.Comment: 15 pages, 3 figures, thoroughly rewritte