A new relativistically covariant approach is discussed for the derivation of local conservation theorems for homogeneous anisotropic and, in particular, dispersive media. We start from a three-dimensional operator equation for the electric field and obtain mainly by coordinate-invariant methods the results basically expressed by the slowly varying amplitudes of the electric field. Apart from local energy and momentum conservation formulated by the energy-momentum conservation, we find a local conservation theorem for the action which is more general and which is the only one which remains also true for inhomogeneous media.
References
[1]
Einstein, A. (1913) Zeitschrift für Angewandte Mathematik und Physik, 62, 225-261.
[2]
Tamm, I.E., Smorodinsky, J.A. and Kuznetsov, B.G. (1965) Albert Einstein, Sobranyje nauchnykh truduv, I (Collection of Scientific Works, Part I). Nauka, Moskva.
[3]
Landau, L.D. and Lifshitz, E.M. (1962) The Classical Theory of Fields (4th Revised Edition). Nauka, Moskva.
[4]
Rashevski, P.K. (1964) Riemann Geometry and Tensor Analysis. 2nd Edition, Nauka, Moskva. (In Russian)
[5]
Pauli, W. (1921) Relativitatstheorie. Enzyklopadie der mathematischen Wissenschaften, Band V, Heft IV, Art. 19, B.G. Teubner, Leipzig.
[6]
Lorentz, H.A., Weyl, H. and Minkowski, H. (1922) Das Relativitatsprinzip, B.G. Teubner, Leipzig. https://doi.org/10.1007/978-3-663-16170-7
[7]
Landau, L.D. and Lifshitz, E.M. (1982) Electrodynamics of Continuous Media. 2nd Edition, Nauka, Moskva.
Tamm, I.Ye. (1976) Osnovy teorii elektrichestva (Foundations of the Theory of Elctricity). 9th Edition, Nauka, Moskva.
[20]
Møller, C. (1972) The Theory of Relativity. Clarendon Press, Oxford.
[21]
Jackson, J.D. (1962) Classical Electrodynamics. John Wiley, New York. https://doi.org/10.1063/1.3057859
[22]
Felsen, L.B. and Marcuvitz, N. (1973) Radiation and Scattering of Waves. Prentice-Hall, Englewood Cleffs.
[23]
Yariv, A. and Yeh, P. (1984) Optical Waves in Crystals. Wiley-Interscience, New York.
[24]
Melrose, D.B. and McPhedran, R.C. (1991) Electromagnetic Processes in Dispersive Media. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511600036
[25]
Jimenez, J.L. and Campos, I. (1995) The Balance Equations of Energy and Momentum in Classical Electrodynamics. In: Barrett, T.W. and Grimes, D.M., Eds., Advanced Electromagnetism, World Scientific, Singapore, 464-495. https://doi.org/10.1142/9789812831323_0016
Wünsche, A. (1970) Annals of Physics (Leipzig), 25, 201-214. https://doi.org/10.1002/andp.19704800207
[31]
Wünsche, A. (1978) Annals of Physics (Leipzig), 35, 303-320. https://doi.org/10.1002/andp.19784900407
[32]
Leonhardt, U. (2000) Physical Review A, 62, Article ID: 012111. https://doi.org/10.1103/PhysRevA.62.012111
[33]
Leonhardt, U. and Piwnicki, P. (2001) Journal of Modern Optics, 48, 977-988. https://doi.org/10.1080/09500340108230969
[34]
Wünsche, A. (2005) Acta Physica Hungarica B, 23, 151-162. https://doi.org/10.1556/APH.23.2005.3-4.5
[35]
Lorentz, H.A. (1904) van Wetenschappen te Amsterdam, 6, 809.
[36]
Tyapkin, A.A. (1973) The Principle of Relativity (with a Preface of D.I. Blokhintsev). Atomisdat, Moscow.15
[37]
Lorentz, H.A. (1904) Weiterbildung der Maxwellschen Theorie. Elektronentheorie. In: Enzyklopadie der mathematischen Wissenschaften, Bd. 2, Teubner, Leipzig, Art. 14, 245.
[38]
Lorentz, H.A. (1915) Theory of Electrons. 2nd Edition, Teubner, Leipzig.
[39]
de Groot, S.R. and Suttorp, L.G. (1972) Foundations of Electrodynamics. North Holland Publ. Comp., Amsterdam.
[40]
Bloembergen, N. (1965) Nonlinear Optics. W.A. Benjamin, Inc., New York.
[41]
Wünsche, A. (1971) Monatsberichte der Deutschen Akademie der Wissenschaften zu Berlin, 13, 479-492.
[42]
Hebenstreit, H. and Suchy, K. (1979) Zeitschrift für Naturforschung A, 34, 1147-1157. https://doi.org/10.1515/zna-1979-1001
[43]
Minkowski, H. (1909) Physikalische Zeitschrift, 10, 104-111.
[44]
Lorentz, H.A., Einstein, A., Minkowski, H. and Weyl, H. (1952) The Principle of Relativity. Dover, Mineola.
[45]
Landau, L.D. and Lifshitz, E.M. (1988) The Classical Theory of Fields. 7nd Edition, Nauka, Moskva.
[46]
Szivessy, G. (1928) Kristalloptik. In: Geiger, H. and Scheel, K., Eds., Handbuch der Physik, Band XX, Springer, Berlin, 635-904. https://doi.org/10.1007/978-3-642-90780-7_11
[47]
Born, M. and Wolf, E. (1999) Principles of Optics. Seventh Edition, Cambridge University Press, Cambridge.
[48]
Ginzburg, V.L. (1974) Kak i kto sozdal teoriyu otnocitel’nosti? (How and Who Created Relativity Theory?) In: Einshteynovski sbornik (Einsteinian Anthology), Nauka, Moscow, 351-384.
