A relativistic one-particle Time of Arrival operator for a free spin-1/21/2 particle in (1+1)(1+1) dimensions

As a follow-up to a recent study in the spin-0 case (Bunao and Galapon, 2015), we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin-1/21/2 particle in one spatial dimension. Upon transformation in a representation where the Hamiltonian is diagonal, it turns out that the constructed operator consists of an operator term Tˆ whose action is the same as in the spin-0 case, and another operator term Tˆ0 which commutes with the Hamiltonian but breaks invariance under parity inversion. If we must impose this symmetry on our TOA operator, then we can throw away Tˆ0 so that the TOA operator is just Tˆ.