DIRAC – KÄHLER PARTICLE IN THE EXTERNAL MAGNETIC FIELD, CYLINDRICAL TETRAD AND FEDOROV – GRONSKIY METHOD - Ivashkevich, Alina; Redʼkov, Viktor (Веснік Брэсцкага ўніверсітэта. Серыя 4. Фізіка. Матэматыка, 2024)
16-component system of equations for the Dirac – Kähler particle in the presence of the external uniform magnetic field has been studied. This equation describes a multi-spin boson field equivalent to the scalar, pseudoscalar, vector, pseudovecto, and antisymmetric tensor. On the searched solutions, we diagonalize operators of the energy, the third projection of the total angular momentum, and the third projection of the linear momentum. After separating the variables, we derive the system of sixteen first order differential equations in polar coordinate. To resolve this system, we apply the method by Fedorov – Gronskiy based on projective operators constructed from generator j12 for the 2-rank bispinor. According to this approach, we decompose the complete wave function into three 16-dimensional projective constituents, each expressed trough only one corresponding function of the polar coordinate. There are imposed additional differential constraints which permit us to transform all equations to algebraic form. Three basic variables are constructed in terms of the confluent hypergeometric functions, at this a quantization rule arises due to the presence of the external magnetic field. The 16-dimensional structure of solutions is determined by the linear algebraic system of equations. We have found five lineraly independent solutions.