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Generation and classification of localized waves by Lorentz transformations in Fourier space

Peeter Saari and Kaido Reivelt

  • Institute of Physics, University of Tartu, Riia 142, 51014 Tartu, Estonia

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Phys. Rev. E 69, 036612 – Published 31 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.036612

Abstract

The Lorentz transformations of propagation-invariant localized waves (also known as nondispersive or nondiffracting or undistorted progressive waves) are studied in the frequency-momentum space. For supports of wave functions in this space rules of transformation are derived which allow one to group all localized waves into distinct classes: subluminal, luminal, and superluminal localized waves. It is shown that for each class there is an inertial frame in which any given localized wave takes a particularly simple form. In other words, any localized wave is nothing but a relativistically aberrated and Doppler shifted version of a simple “seed” wave. Also discussed are the relations of the physical (subluminal) Lorentz tranformation to other mathematical tranformations used in the literature on localized waves, as well as physical interpretation of the substantial changes that localized waves undergo if observed and generated in different inertial frames.

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Phys. Rev. E 69, 036612– Published 31 March, 2004
  • Received 15 August 2003

© 2004 American Physical Society

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