Abstract
Identifying invariance properties helps in simplifying calculations and consolidating concepts. Presently the Special Relativistic invariance of dispersion relations and their associated scalar wave operators is investigated for general dispersive homogeneous linear media. Invariance properties of the four-dimensional Fourier-transform integrals is demonstrated, from which the invariance of the scalar Green-function is inferred Dispersion relations and the associated group velocities feature in Hamiltonian ray tracing theory. The derivation of group velocities for moving media from the dispersion relation for these media at rest is discussed. It is verified that the group velocity concept satisfies the relativistic velocity-addition formula. In this respect it is considered to be 'real', i.e., substantial, physically measurable, and not merely a mathematical artifact. Conversely, if we assume the group velocity to be substantial, it follows that the dispersion relation must be a relativistic invariant.
Original language | English |
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Pages (from-to) | 194-202 |
Number of pages | 9 |
Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |
Volume | 90 |
Issue number | 3 |
DOIs | |
State | Published - 1 Mar 2010 |
Keywords
- Electromagnetic theory
- Electromagnetic wave propagation
- Relativistic electrodynamics
ASJC Scopus subject areas
- Computational Mechanics
- Applied Mathematics