Relativistic invariance of dispersion-relations and their associated wave-operators and Green-functions

Dan Censor

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 Fouriertransform 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 is a proper velocity, satisfying the relativistic transformation formula for velocities. Conversely, if we assume the group velocity to be a true (e.g., mechanical) velocity, then it follows that the dispersion relation must be a relativistic invariant.

Original languageEnglish
Title of host publication2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Pages255-259
Number of pages5
DOIs
StatePublished - 1 Dec 2008
Event2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008 - Eilat, Israel
Duration: 3 Dec 20085 Dec 2008

Publication series

NameIEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings

Conference

Conference2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Country/TerritoryIsrael
CityEilat
Period3/12/085/12/08

Keywords

  • Electromagnetic theory
  • Special relativity
  • Wave propagation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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