volume | PIER Journals

Abstract

A type of closed exterior algebra in R³ under the cross product is revealed to hold between differential forms from the three Whittaker scalar potentials, associated with the fields of a moving electron. A special algebraic structure is revealed in the context of Clebsch reparametrization of these scalars, and a special prescription for the construction of permutation invariant electromagnetic fields is given as well as a superposition with parallel electric and magnetic components.

1. Whittaker, E. T., "On an expression of the electromagnetic field due to electrons by means of two scalar potential functions," Proc. London Math. Soc., Vol. 1, 367-372, 1904.
doi:10.1112/plms/s2-1.1.367 Google Scholar

2. Bateman, H., "The solution of partial differential equations by means of definite integrals," Proc. London Math. Soc., Vol. 1, No. 1, 451-458, 1904.

3. Ruse, H. S., "The geometry of the electromagnetic six-vector, the electromagnetic energy and the Hertzian tensor," C. R. Congr. Internat. Math., Vol. 2, 232, 1936. Google Scholar

4. Ruse, H. S., "On Whittaker's electromagnetic scalar potentials," Quart. J. Math. Soc., Vol. 8, No. 1, 148-160, 1937.
doi:10.1093/qmath/os-8.1.148 Google Scholar

5. Kawaguchi, H. and S. Murata, "Hertzian tensor potential which results in Lienard-Wiechert potential," J. Phys. Soc. Jap., Vol. 58, No. 3, 848-855, 1989.
doi:10.1143/JPSJ.58.848 Google Scholar

6. Kawaguchi, H. and T. Honma, "On the super-potentials for Lienard-Wiechert potentials in far fields," J. Phys. A: Math. Gen., Vol. 25, 4437, 1992.
doi:10.1088/0305-4470/25/16/019 Google Scholar

7. Kawaguchi, H. and T. Honma, "Superpotentials of Lienard-Wiechert potentials in far fields: The relativistic case," J. Phys. A: Math. Gen., Vol. 26, No. 17, 4431, 1993.
doi:10.1088/0305-4470/26/17/047 Google Scholar

8. Kawaguchi, H. and T. Honma, "On a double fiber bundle structure of the Lienard-Wiechert superpotentials," J. Tech. Phys., Vol. 35, No. 1-2, 61-65, 1994. Google Scholar

9. Kawaguchi, H. and T. Honma, "On the electrodynamics of the Lienard-Wiechert superpotentials," J. Phys. A: Math. Gen., Vol. 28, No. 2, 469, 1995.
doi:10.1088/0305-4470/28/2/021 Google Scholar

10. Marmanis, H., Analogy between the electromagnetic and hydrodynamic equations: Applications to turbulence, Ph.D.Thesis, Brown University, 1999.

11. Martins, A. A. and M. J. Pinheiro, "Fluidic electrodynamics: Approach to electromagnetic propulsion," Phys. Fluids, Vol. 21, 097103, 2001. Google Scholar

12. Bateman, H., Partial Differential Equations of Mathematical Physics, Cambridge Univ. Press, 1959.

13. Stern, D. P., "Euler potentials," Am. J. Phys., Vol. 38, No. 4, 494-501, 1970.
doi:10.1119/1.1976373 Google Scholar

14. Asanov, G. S., "Clebsch representations and energy-momentum of classical electromagnetic and gravitational fields," Found. Phys., Vol. 10, No. 11-12, 855-863, 1980.
doi:10.1007/BF00708684 Google Scholar

15. Marsden, J. and A. Weinstein, "Coadjoint orbits, vortices and Clebsch variables for incompressible fluids," Physica D, Vol. 7, 305-323, 1983.
doi:10.1016/0167-2789(83)90134-3 Google Scholar

16. Ranada, A. F., "Interplay of topology and quantization: Topological energy quantization in a cavity," Phys. Lett. A, Vol. 310, 434, 2003.
doi:10.1016/S0375-9601(03)00443-2 Google Scholar

17. Uehara, K., et al. "Non-transverse electromagnetic fields with parallel electric and magnetic fields," J. Phys. Soc. Jap., Vol. 58, No. 10, 3570-3575, 1989.
doi:10.1143/JPSJ.58.3570 Google Scholar

18. Shimoda, K., et al. "Electromagnetic plane waves with parallel electric and magnetic fields E||B in free space," Am. J. Phys., Vol. 58, No. 4, 394, 1990.
doi:10.1119/1.16482 Google Scholar

19. Gray, J. E., "Electromagnetic waves with E parallel to B," J. Phys. A: Math. Gen., Vol. 25, No. 20, 5373, 1992.
doi:10.1088/0305-4470/25/20/017 Google Scholar

Mr. Theophanes E. Raptis