Velocity Operators and Time-Energy Relations in Relativistic Quantum Mechanics

According to both Dirac's and Kemmer's relativistic quantum theories, the eigenvalues of the velocity operator are +c and –c. This false result is avoided if certain alternative particle coordinates are adopted. Another advantage is that the new coordinates occur in additional constants of the motion. These are sui generis angular momenta obtained by taking the vector product of the nonstandard coordinates with the linear momentum. An additional virtue of the new velocity operator is that, like in classical mechanics, it is proportional to the linear momentum. Besides, the zeroth component of the new set of coordinates does not commute with the hamiltonian, which results in a genuine indeterminacy relation between time and energy.