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Generation and classification of localized waves by Lorentz transformations in Fourier space
1Institute of Physics, University of Tartu, Riia 142, 51014 Tartu, Estonia.
Summary
Localized waves, including nondiffracting waves, are classified into subluminal, luminal, and superluminal types using Lorentz transformations. Each class simplifies in a specific inertial frame, revealing them as transformed versions of basic "seed" waves.
Area of Science:
- Physics
- Wave Phenomena
- Relativity
Background:
- Localized waves, such as nondiffracting waves, exhibit unique propagation properties.
- Understanding their behavior under relativistic transformations is crucial for advanced wave physics.
Purpose of the Study:
- To investigate the Lorentz transformations of localized waves in frequency-momentum space.
- To classify these waves based on their relativistic properties and identify simplified forms in specific frames.
Main Methods:
- Derivation of transformation rules for wave function supports in frequency-momentum space.
- Application of Lorentz transformations to analyze wave behavior across different inertial frames.
Main Results:
- Classification of localized waves into subluminal, luminal, and superluminal categories.
- Demonstration that each wave class simplifies in a particular inertial frame.
- Identification of localized waves as relativistically transformed and Doppler-shifted 'seed' waves.
Conclusions:
- Lorentz transformations provide a unifying framework for understanding diverse localized wave behaviors.
- The study offers insights into the physical interpretation of wave transformations across inertial frames.