We are interested in the energy-momentum relation for a moving composite in relativistic quantum mechanics in many-particle Dirac models. For a manifestly covariant model one can apply the Lorentz transform to go from the rest frame to a moving frame to establish an energy-momentum relation of the form $\sqrt{ (M^*c^2)^2+c^2|{ \bf P}|^2}$ where $M^*$ is the kinematic mass. However, the many-particle Dirac model is not manifestly covariant, and some other approach is required. We have found a simple approach that allows for a separation of relative and center of mass contributions to the energy. We are able to define the associated kinematic energy and determine the energy-momentum relation. Our result can be expressed as a modified deBroglie relation of the form $$ \hbar \omega ({ \bf P}) = <\Phi' | \sum_j { m_j \over M} \beta_j | \Phi' >~ \sqrt{ [M^*({ \bf P}) c^2]^2 + c^2 |{ \bf P}|^2} $$ where the kinematic mass $M^*$ will depend on the total momentum ${ \bf P}$ for a general noncovariant potential. The prefactor that occurs we associate with a time dilation effect, the existence of which has been discussed previously in the literature.
Categories: cond-mat.other