  In this paper a generalized form of relativistic dynamics is presented: A
realization of the Poincar\'e algebra is provided in terms of vector fields on
the tangent bundle of a simultaneity surface in $\mathbb{R}^4$. The
construction of this realization is explicitly shown to clarify the role of the
commutation relations of the Poincar\'e algebra versus their description in
terms of Poisson brackets in the no-interaction theorem. Moreover, a
geometrical analysis of the ``eleventh generator'' formalism introduced by
Sudarshan and Mukunda is outlined, this formalism being at the basis of many
proposals which evaded the no-interaction theorem.
