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

Dan Censor

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)194-202
Number of pages9
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Issue number3
StatePublished - 1 Mar 2010


  • Electromagnetic theory
  • Electromagnetic wave propagation
  • Relativistic electrodynamics

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics


Dive into the research topics of 'Relativistic invariance of dispersion-relations and their associated wave-operators and Green-functions'. Together they form a unique fingerprint.

Cite this