The supposition of the manifest covariance of average trajectory world lines is violated in Hamiltonian formulations of relativistic quantum mechanics. This is due to the nonlinear appearance of particle dynamical variable operators in the Heisenberg picture boosted position, velocity, and momentum operators. The magnitude of this deviation from world line manifest covariance is found to be exceedingly small for a number of common time of flight experiments.
The Transformation Properties of World Lines in Relativistic Quantum Mechanical Hamiltonian ModelsFoundations of Physics
Citation InformationLock, J. A. (1982). The transformation properties of world lines in relativistic quantum mechanical Hamiltonian models. Foundations of Physics, 12(8), 743 - 757.