Dirac equation in five dimensions

Dirac equation in a covariant form with respect to proper orthochronous rotations in (4+1)-dimensional pseudo-orthogonal space, i.e. Minkowski space extended by one real dimension is introduced. It is invariant under the CPT transformation if the real fifth coordinate is odd under charge conjugation and time reversal and is even under space inversion. A function constructed from Jacobian elliptic functions replaces exp(iwt). In the limit of a vanishing modulus of these functions, the influence of the fifth dimension on the energy levels of an electron in Coulomb and gravitational field can be neglected. The iterated five-dimensional Dirac equation contains the potential energy of electron spin in a non-electromagnetic field.