Saari Peeter, Reivelt Kaido
Institute of Physics, University of Tartu, Riia 142, 51014 Tartu, Estonia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):036612. doi: 10.1103/PhysRevE.69.036612. Epub 2004 Mar 31.
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 aberrant 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.
在频动量空间中研究了传播不变局域波（也称为非色散、非衍射或无畸变行波）的洛伦兹变换。对于该空间中波函数的支集，推导了变换规则，这些规则允许将所有局域波分为不同的类别：亚光速、光速和超光速局域波。结果表明，对于每一类，都存在一个惯性系，在其中任何给定的局域波都具有特别简单的形式。换句话说，任何局域波都只不过是一个简单 “种子” 波的相对论性畸变和多普勒频移版本。还讨论了物理（亚光速）洛伦兹变换与局域波文献中使用的其他数学变换的关系，以及如果在不同惯性系中观察和产生局域波时，局域波所经历的实质性变化的物理解释。
