present in the one-body Dirac equation and vanish when one of the particles becomes very heavy (the so-called static limit). More on constraint dynamics: generalized mass shell constraints Constraint dynamics arose from the work of Dirac and Bergmann. This section shows how the elimination of relative time and energy takes place in the c.m. system for the simple system of two relativistic spinless particles. Constraint dynamics was first applied to the classical relativistic two particle system by Todorov, Kalb and Van Alstine, Komar, and Droz–Vincent. With constraint dynamics, these authors found a consistent and covariant approach to relativistic canonical Hamiltonian mechanics that also evades the Currie–Jordan–Sudarshan "No Interaction" theorem. That theorem states that without fields, one cannot have a relativistic Hamiltonian dynamics. Thus, the same covariant three-dimensional approach which allows the quantized version of constraint dynamics to remove quantum ghosts simultaneously circumvents at the classical level the C.J.S. theorem. Consider a constraint on the otherwise independent coordinate and momentum four vectors, written in the form . The symbol is called a weak equality and implies that the constraint is to be imposed only after any needed Poisson brackets are performed. In the presence of such constraints, the total Hamiltonian is obtained from the Lagrangian by adding to the Legendre Hamiltonian the sum of the constraints times an appropriate set of Lagrange multipliers . , This total Hamiltonian is traditionally called the Dirac Hamiltonian. Constraints arise naturally from parameter invariant actions of the form In the case of four vector and Lorentz scalar interactions for a single particle the Lagrangian is The canonical momentum is and by squaring leads to the generalized mass shell condition or generalized mass shell constraint Since, in this case, the Legendre Hamiltonian vanishes the Dirac Hamiltonian is simply the generalized mass constraint (with no interactions it would simply be the ordinary mass shell constraint) One then postulates that for two bodies the Dirac Hamiltonian is the sum of two such mass shell constraints, that is and that each constraint be constant in the proper time associated with Here the weak equality means that the Poisson bracket could result in terms proportional one of the constraints, the classical Poisson brackets for the relativistic two-body system being defined by To see the consequences of having each constraint be a constant of the motion, take, for example Since and and one has The simplest solution to this is which