TY - JOUR

T1 - Lorentz-boost eigenmodes

AU - Bliokh, Konstantin Y.

N1 - Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/7/30

Y1 - 2018/7/30

N2 - 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 (spatiotemporal 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 steplike 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.

AB - 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 (spatiotemporal 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 steplike 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.

UR - http://www.scopus.com/inward/record.url?scp=85051205076&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.012143

DO - 10.1103/PhysRevA.98.012143

M3 - Article

SN - 2469-9926

VL - 98

JO - Physical Review A

JF - Physical Review A

IS - 1

M1 - 012143

ER -