  In this paper, we revisit the aquisition of angular momentum of galaxies by
tidal shearing and compute the angular momentum variance sigma_L^2 as well as
the angular momentum correlation function C_L(r) from a peak-restricted
Gaussian random process. This stochastic process describing the initial
conditions treats both the tidal shear as well as the inertia as dynamical
fields and explicitly accounts for the discreteness of the inertia field. We
describe the way in which the correlations in angular momentum result from an
interplay of long-ranged correlations in the tidal shear, and short ranged
correlations in the inertia field and which reflects the correlation between
the eigensystems of these two symmetric tensors. We propose a new form of the
angular momentum correlation function which is able to distinguish between
parallel and antiparallel alignment of angular momentum vectors, and comment on
implications of intrinsic alignments for weak lensing measurements. We confirm
the scaling L/M propto. M^{2/3} and find the angular momentum distribution of
Milky Way-sized haloes to be correlated on scales of ~1 Mpc/h. The correlation
function can be well fitted by an empirical relation of the form C_L(r) propto.
exp(-[r/r_0]^beta).
