  We derive a closed formula for the matrix elements of the volume operator for
canonical Lorentzian quantum gravity in four spacetime dimensions in the
continuum in a spin-network basis. We also display a new technique of
regularization which is state dependent but we are forced to it in order to
maintain diffeomorphism covariance and in that sense it is natural. We arrive
naturally at the expression for the volume operator as defined by Ashtekar and
Lewandowski up to a state independent factor.
