The effect of a canonical Lorentz boost on the Newton-Wigner-Pryce position operator of a spin zero system is calculated. The resulting equations differ significantly from those corresponding to the Lorentz boost of a position coordinate in classical special relativity. The components of the boosted Newton-Wigner-Pryce position operator are interpreted in terms of a classical analog. It is seen that the transformed operator corresponds not to the coordinates of the same event in two reference frames, but to the coordinates of the intersection of the worldline of the system's center of momentum with hyperplanes of the same coordinate time in the two frames.The effect of a canonical Lorentz boost on the Newton-Wigner-Pryce position operator of a spin zero system is calculated. The resulting equations differ significantly from those corresponding to the Lorentz boost of a position coordinate in classical special relativity. The components of the boosted Newton-Wigner-Pryce position operator are interpreted in terms of a classical analog. It is seen that the transformed operator corresponds not to the coordinates of the same event in two reference frames, but to the coordinates of the intersection of the worldline of the system's center of momentum with hyperplanes of the same coordinate time in the two frames.

Physical Review AOct 1, 19977 citations

The Lorentz Atom

Mark Linne

Elsevier eBooksJan 1, 20020 citations

Lorentz-boost eigenmodes

Konstantin Yu Bliokh

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.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.

arXiv:1802.03940Physical Review AJul 30, 201811 citations

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.