Безмассовая частица Штюкельберга, решения с цилиндрической симметрией

Abstract

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.