Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem

We provide a full account of our recent report (Flores and Galapon in EPL 141:10001, 2023) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a square barrier. It was shown that the tunneling time of a relativistic spin-0 particle is instantaneous under the condition that the barrier height V-o is less than the rest mass energy. This implies that instantaneous tunneling is an inherent quantum effect in the context of arrival times.