Lorentz-boost eigenmodes
Abstract
Plane waves and cylindrical or spherical vortex modes are important sets of solutions of quantum and classical wave equations. These are eigenmodes of the energy-momentum and angular-momentum operators, i.e., generators of spacetime translations and spatial rotations, respectively. Here we describe another set of wave modes: eigenmodes of the "boost momentum" operator, i.e., a generator of Lorentz boosts (spatio-temporal rotations). Akin to the angular momentum, only one (say, z) component of the boost momentum can have a well-defined quantum number. The boost eigenmodes exhibit invariance with respect to the Lorentz transformations along the z-axis, leading to scale-invariant wave forms and step-like singularities moving with the speed of light. We describe basic properties of the Lorentz-boost eigenmodes and argue that these can serve as a convenient basis for problems involving causal propagation of signals.
Cite
@article{arxiv.1802.03940,
title = {Lorentz-boost eigenmodes},
author = {Konstantin Y. Bliokh},
journal= {arXiv preprint arXiv:1802.03940},
year = {2018}
}
Comments
16 pages, 4 figures, to appear in Phys. Rev. A