Time Operator in Relativistic Quantum Mechanics

It is first shown that the Dirac＇s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 x 4 relativistic time operator for spin-l/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly sma/l but non- zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli＇s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.