  We consider a one-dimensional wire in gaussian random potential. By treating
the spatial direction as imaginary time, we construct a `minimal'
zero-dimensional quantum system such that the local statistical properties of
the wire are given as products of statistically independent matrix elements of
the evolution operator of the system. The space of states of this quantum
system is found to be a particular non-unitary, infinite dimensional
representation of the pseudo-unitary group, U(1,1). We show that our
construction is minimal in a well defined sense, and compare it to the
supersymmetry and Berezinskii techniques.
