A strange weak value in spontaneous pair productions via a supercritical step potential

We consider a case when a weak value is introduced as a physical quantity rather than as an average of weak measurements. The case we treat is a time evolution of a particle by the 1 + 1-dimensional Dirac equation. In particular, in a spontaneous pair production via a supercritical step potential, a quantitative explanation can be given by a weak value for the group velocity of the particle. We also show that the condition for the pair production (supercriticality) corresponds to the condition when the weak value takes a strange value (superluminal velocity). (paper)