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Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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A VARIABLE METRIC ELECTRODYNAMICS. PLANE WAVES

By B. Jancewicz

Full Article PDF (233 KB)

Abstract:
Classical electrodynamics can be divided into two parts. In the first one, a need of introducing a plenty of directed quantities occurs, namely multivectors and differential forms but no scalar product is necessary. We call it premetric electrodynamics. In this part, principal equations of the theory can be tackled. The second part concerns solutions of the equations and requires establishing of a scalar product and, consequently, a metric. For anisotropic media two scalar products can be introduced depending on the electric permittivity and magnetic permeability tensors. In the case of plane electromagnetic waves both of them are needed because two constitutive equations are needed: one for the electric fields, the other for the magnetic field. We show which part of the description of plane electromagnetic waves is independent of scalar products, and where they become necessary.

Citation:
B. Jancewicz, "A Variable Metric Electrodynamics. Plane Waves," Progress In Electromagnetics Research, Vol. 36, 279-317, 2002.
doi:10.2528/PIER02032604
http://www.jpier.org/PIER/pier.php?paper=0203264

References:
1. Grauert, H. and I. Lieb, Differential und Integralrechnung, Vol. 3, Springer Verlag, Berlin, 1968.

2. Misner, C., K. Thorne, and J. A. Wheeler, Gravitation, Sec. 2.5, Freeman and Co., San Francisco, 1973.

3. Thirring, W., Course in Mathematical Physics, Vol. 2, Classical Field Theory, Springer Verlag, New York, 1979.

4. Deschamps, G. A., "Electromagnetics and differential forms," Proc. IEEE, Vol. 69, 676-696, 1981.
doi:10.1109/PROC.1981.12048

5. Schouten, J. A., Tensor Analysis for Physicists, Dover Publ., New York, 1989, (first edition: Clarendon Press, Oxford 1951).

6. Frankel, T., Gravitational Curvature. An Introduction to Einstein’s Theory, Freeman and Co., San Francisco, 1979.

7. Meetz, K. and W. L. Engel, Elektromagnetische Felder, Springer Verlag, Berlin, 1980.
doi:10.1007/978-3-642-86551-0

8. Burke, W. L., "Spacetime, Geometry, Cosmology," University Science Books, Mill Valley, 1980.

9. Burke, W. L., Applied Differential Geometry, Cambridge University Press, Cambridge, 1985.
doi:10.1017/CBO9781139171786

10. Ingarden, R. and A. JamioÃlkowski, Classical Electrodynamics, Elsievier, Amsterdam, 1985.

11. Warnick, K. F. and D. V. Arnold, "Electromagnetic Green functions using differential forms," J. Electrom. Waves Appl., Vol. 10, 427-438, 1996.
doi:10.1163/156939396X00504

12. Hehl, F. W. and Y. N. Obukhov, Foundations of Classical Electrodynamics, Birkhauser Verlag, Boston, 2001.

13. Jancewicz, B., "A variable metric electrodynamics. the Coulomb and Biot-Savart laws in anisotropic media," Ann. Phys., Vol. 245, 227-274, 1996.
doi:10.1006/aphy.1996.0009

14. Warnick, K. F. and D. V. Arnold, "Green forms for anisotropic inhomogeneous media," J. Electrom. Waves Appl., Vol. 11, 1145-1164, 1997.
doi:10.1163/156939397X01061

15. Teixeira, F. L. and W. C. Chew, "Differential forms, metrics, and the reflectionless absorption of electromagnetic waves," J. Electrom. Waves Appl., Vol. 13, 665-686, 1999.
doi:10.1163/156939399X01104

16. Obukhov, Y. N. and F. W. Hehl, "Spacetime metric from linear electrodynamics," Physics Letters B, Vol. 458, 466-470, 1999.
doi:10.1016/S0370-2693(99)00643-7

17. Lounesto, P., R. Mikkola, and V. Vierros, "Geometric algebra software for teching complex numbers, vectors and spinors," J. of Computers in Math. and Science Teaching, Vol. 9, 93-105, 1989.

18. Boulanger, Ph. and M. Hayes, "Electromagnetic plane waves in anistrotropic media," Phil. Trans. R. Soc. London, Vol. A330, 335-393, 1990.
doi:10.1098/rsta.1990.0018

19. Landau, L. D. and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Oxford, 1984.


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