Calb – Ramond Field, Solutions with Spherical Symmetry, the Gauge Degrees of Freedom
Article Sidebar
Main Article Content
Abstract
In the present paper, the system of 10 equations for Calb – Ramond particle is studied in spherical coordinates. For this particle, in contrast to Maxwell theory, the antisymmetric tensor represents gauge variables, and 4-vector relates to physically observable ones. After separating the variables we get the first order system of 10 radial equations. By diagonalysing the space reflection operator, we get to more simple subsystems of 4 and 6 equations, related to states with parities P = (–1)j+1 and P = (–1)j respectively. For parity P = (–1)j+1 the system of 4 equations has two independent solutions, they both describe two gauge states. For parity P = (–1)j, the system of 6 equations has 2 independent solutions; one of them is purely gauge, and the other includes both observable and gauge variables. Therefore, for Calb – Ramond particle there exist only one physically observable state with spherical symmetry, and three states are gauge ones. Recall that in Maxwell theory, exist 2 physically observable states, and 2 pure gauge states.
Article Details
References
1. Огиевецкий, В. И. Нотоф и его возможные взаимодействия / В. И. Огиевецкий, И. В. Полубаринов // Ядерная физика. – 1966. – Т. 4, вып. 1. – С. 216–223.
2. Kalb, M. Classical direct interstring action / M. Kalb, P. Ramond // Phys. Rev. D. – 1974. – Vol. 9. – P. 2273–2284.
3. Berche, B. Classical Kalb – Ramond field theory in curved space-times / B. Berche, S. Fumeron, F. Moraes // Phys. Rev. D. – Vol. 105, nr 1. – Paper 105026.
4. Hell, A. On the duality of massive Kalb – Ramond and Proca fields / A. Hell // Journal of Cosmology and Astroparticle Physics. – 2022. – Vol. 01. – Paper 056.
5. Stuckelberg particle in the Coulomb field, non-relativistic approximation, wave functions and spectra / E. M. Ovsiyuk, O. A Semenyuk, A. V. Ivashkevich, M. Neagu // Nonlinear Phenomena in Complex Systems. – 2022. – Vol. 25, nr 4. – P. 387–404.
6. Stueckelberg, E. C. G. Die Wechselwirkungskräfte in der Elektrodynamik und in der Feldtheorie der Kernkräfte / E. C. G. Stueckelberg // Helv. Phys. Acta. – 1938. – Vol. 11. – P. 299–328.
7. Ruegg, H. The Stueckelberg field / H. Ruegg, M. Ruiz-Altabal // Int. J. Mod. Phys. A. – 2004. – Vol. 119. – P. 3265–3348.