Relativistic free motion time of arrival operator for massive spin-0 particles with positive energy

Abstract

A relativistic version of the Aharonov-Bohm time of arrival operator for spin-0 particles was constructed by Razavi in [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time of arrival problem that goes beyond Razavi's original results. This allows us to use time of arrival eigenfunctions that exhibit unitary arrival to construct time of arrival distributions. The expectation value is also calculated and shown to have quantum correction terms which can cause a particle to either arrive earlier or later than expected. Lastly, the constructed TOA distribution and TOA expectation value are shown to be consistent with special relativity.