Massless Stueckelberg particle, solutions with cylindric symmetry

The massless Stueckelberg field is studied in cylindrical coordinates. The field function consists of the scalar, 4-vector, and antisymmetric tensor. Physically observable components are the scalar and 4-vector. We apply the Stueckelberg tetrad-based matrix equation, generalized to arbitrary Riemannian space, including any curvilinear coordinates in the Minkowski space. We construct solutions with cylindric symmetry, while the operators of energy, of the third projection of the total angular momentum, and the third projection of the linear momentum are diagonalized. After separating the variables we derive the system of 11 first-order differential equations in polar coordinate. It is solved with the use of the Fedorov–Gronskiy method. According to this method, all 11 functions are expressed through 3 main funcions. According to the known procedure we impose the differential constraints, which are consistent with the all 11 equations and allow us to transform these equations to algebraic form. This algebraic system is solved by standard methods. As a result, we obtain 5 linearly independent solutions. The problem of eliminating the gauge solutions will be studied in a separate paper.