Dirac – Kähler Particle in the Uniform Electric Field, Solutions With Cylindrical Symmetry

16-component system of equations describing the Dirac – Kähler particle in presence of the external electric field has been studied. This equation describes a multi-spin boson field equivalent to the scalar, pseudoscalar, vector, pseudovector,and anti-symmetric tensor. On the searched solutions, the operators of the energy and the third projection of the total angular momentum are diagonalized. After separating the variables in cylindrical coordinates, the system of sixteen first order equations in partial derivative with respect to coordinates (r, z) is derived. To resolve this system the method by Fedorov – Gronskiy is applied. Correspondingly, the complete wave function is decomposed into the sum of three projective constituents. Dependence of 16 variables on the polar coordinate is determined only through three basic functions Fi(r) , at this there arise differential constrains which permit to derive the system of 16 differential equations in the coordinate z. The three basic variables are found in terms of Bessel functions. The system of equations in the variable z is solved exactly, as the result, four linearly independent solutions for the Dirac – Kähler particle in presence of the external uniform electric field are constructed.