  The use of $\sum \exp(iS[x])$ as the generic form for a sum over histories in
configuration space is discussed critically and placed in its proper context.
The standard derivation of the sum over paths by discretizing the paths is
reviewed, and it is shown that the form $\sum \exp(iS[x])$ is justified only
for Schrodinger-type systems which are at most second order in the momenta.
Extending this derivation to the relativistic free particle, the causal Green's
function is expressed as a sum over timelike paths, and the Feynman Green's
function is expressed both as a sum over paths which only go one way in time
and as a sum over paths which move forward and backward in time. The weighting
of the paths is shown not to be $\exp(iS[x])$ in any of these cases. The role
of the inner product and the operator ordering of the wave equation in defining
the sum over histories is discussed.
