  In the first quantised description of strings, we integrate over target space
co-ordinates $X^\mu$ and world sheet metrics $g_{\alpha\beta}$. Such path
integrals give scattering amplitudes between the `in' and `out' vacuua for a
time-dependent target space geometry. For a complete description of
  `particle creation' and the corresponding backreaction, we need instead the
causal amplitudes obtained from an `initial value formulation'. We argue, using
the analogy of a scalar particle in curved space, that in the first quantised
path integral one should integrate over $X^\mu$ and world sheet {\it
zweibiens}. This extended formalism can be made to yield causal amplitudes; it
also naturally allows incorporation of density matrices in a covariant manner.
(This paper is an expanded version of hep-th 9301044)
