Affiliation:
1. Brest State University named after A.S. Pushkin
2. B.I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
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.
Subject
General Earth and Planetary Sciences,General Energy
Reference11 articles.
1. Duffin, R.I. On the characteristic matrices of the covariant systems / R.I. Duffin // Phys. Rev. – 1938. – Vol. 54, № 12. – P. 1114–1117., Duffin, R.I. On the characteristic matrices of the covariant systems / R.I. Duffin // Phys. Rev. – 1938. – Vol. 54, № 12. – P. 1114–1117.
2. Kemer, N. The particle aspect of meson theory / N. Kemmer // Proc. Roy. Soc. London. A. – 1939. - Vol. 173. – P. 91–116., Kemer, N. The particle aspect of meson theory / N. Kemmer // Proc. Roy. Soc. London. A. – 1939. - Vol. 173. – P. 91–116.
3. Огивецкий, В.И. Нотоф и его возможные взаимодействия / В.И. Огивецкий, И.В. Полубаринов // Ядерная физика. - 1966. - Т. 4, вып. 1. – С. 216–223., Ogiveckiy, V.I. Notof i ego vozmozhnye vzaimodeystviya / V.I. Ogiveckiy, I.V. Polubarinov // Yadernaya fizika. - 1966. - T. 4, vyp. 1. – S. 216–223.
4. Stueckelberg, E.C.G. Die Wechselwirkungskräfte in der Elektrodynamik und in der Feldtheorie der Kernkräfte (Teil II und III) / E.C.G. Stueckelberg // Helv. Phys. Acta. – 1938. – Vol. 11. – P. 299–312, 312–328., Stueckelberg, E.C.G. Die Wechselwirkungskräfte in der Elektrodynamik und in der Feldtheorie der Kernkräfte (Teil II und III) / E.C.G. Stueckelberg // Helv. Phys. Acta. – 1938. – Vol. 11. – P. 299–312, 312–328.
5. Ruegg, H. The Stueckelberg field / H. Ruegg, M. Ruiz- Altabal // Int. J. Mod. Phys. A. – 2004. – Vol. 119. – P. 3265–3348., Ruegg, H. The Stueckelberg field / H. Ruegg, M. Ruiz- Altabal // Int. J. Mod. Phys. A. – 2004. – Vol. 119. – P. 3265–3348.