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

A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [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 that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.

Automated summary

This paper studies the relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles, and provides insights beyond the original results by taking its rigged Hilbert space extension. Time-of-arrival distributions are constructed using eigenfunctions that exhibit unitary arrival, and the expectation value is calculated, showing that particles can arrive earlier or later than expected classically. The constructed time-of-arrival distribution and expectation value are also consistent with special relativity.