  We study reparametrization-invariant systems, mainly the relativistic
particle and its D-dimensional extended object generalization--d-brane. The
corresponding matter Lagrangians naturally contain background interactions,
like electromagnetism and gravity. For a d-brane that doesn't alter the
background fields, we define non-relativistic equations assuming integral
sub-manifold embedding of the d-brane. The mass-shell constraint and the
Klein-Gordon equation are shown to be universal when gravity-like interaction
is present. Our approach to the Dirac equation follows Rund's technique for the
algebra of the $\gamma $-matrices that doesn't rely on the Klein-Gordon
equation.
