A Relativistic Conserved Current Subject to Constraints to Cancel Marginal Negative Probability Values

The bispinor solution to the Dirac equation is used to construct a conserved current. The possibility that the conserved current can take on marginal negative values is addressed as a condition that can be set and altered with constraints. Specifically, a Dirac bispinor solution is constructed and subject to constraints such that the marginal negative probability value in the corresponding conserved current is cancelled completely. Unexpectedly, and for a superposition of positive- and negative-energy states using these bispinor solutions, the conserved current derived here is shown to be completely absent of all Zitterbewegung terms. Various uses of the conserved current and the bispinor solutions derived here are also illustrated in conventional contexts, such as in computing scattering amplitudes across barrier potentials.