  We will construct a non-separable Hilbert space for which the inhomogeneous
${\rm SL}(2,\mathbb{C})$ acts on it unitarily. Each vector in this Hilbert
space is described by a (rectangular) space-like surface in $\mathbb{R}^4$, for
which a frame consisting of a time-like vector and a space-like vector, and a
vector field is defined on it. The inner product on this Hilbert space is
defined via a surface integral, which is associated with the area of the
surface.
