to the 4-component one-body Dirac equation for particle one in an external potential. In SI units: where c is the speed of light and Natural units will be used below. A tilde symbol is used over the two sets of potentials to indicate that they may have additional gamma matrix dependencies not present in the one-body Dirac equation. Any coupling constants such as the electron charge are embodied in the vector potentials. Constraint dynamics and the TBDE Constraint dynamics applied to the TBDE requires a particular form of mathematical consistency: the two Dirac operators must commute with each other. This is plausible if one views the two equations as two compatible constraints on the wave function. (See the discussion below on constraint dynamics.) If the two operators did not commute, (as, e.g., with the coordinate and momentum operators ) then the constraints would not be compatible (one could not e.g., have a wave function that satisfied both and ). This mathematical consistency or compatibility leads to three important properties of the TBDE. The first is a condition that eliminates the dependence on the relative time in the center of momentum (c.m.) frame defined by . (The variable is the total energy in the c.m. frame.) Stated another way, the relative time is eliminated in a covariant way. In particular, for the two operators to commute, the scalar and four-vector potentials can depend on the relative coordinate only through its component orthogonal to in which This implies that in the c.m. frame , which has zero time component. Secondly, the mathematical consistency condition also eliminates the relative energy in the c.m. frame. It does this by imposing on each Dirac operator a structure such that in a particular combination they lead to this interaction independent form, eliminating in a covariant way the relative energy. In this expression is the relative momentum having the form for equal masses. In the c.m. frame (), the time component of the relative momentum, that is the relative energy, is thus eliminated. in the sense that . A third consequence of the mathematical consistency is that each of the world scalar and four vector potentials has a term with a fixed dependence on and in addition to the gamma matrix independent forms of and which appear in the ordinary one-body Dirac equation for scalar and vector potentials. These extra terms correspond to additional recoil spin-dependence not