  The recently developed auxiliary field diffusion Monte Carlo method is
applied to compute the equation of state and the compressibility of neutron
matter. By combining diffusion Monte Carlo for the spatial degrees of freedom
and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum
Monte Carlo can be used to simulate the ground state of many nucleon systems
$(A\alt 100)$. We use a path constraint to control the fermion sign problem. We
have made simulations for realistic interactions, which include tensor and
spin--orbit two--body potentials as well as three-nucleon forces. The Argonne
$v_8'$ and $v_6'$ two nucleon potentials plus the Urbana or Illinois
three-nucleon potentials have been used in our calculations. We compare with
fermion hypernetted chain results. We report results of a Periodic Box--FHNC
calculation, which is also used to estimate the finite size corrections to our
quantum Monte Carlo simulations. Our AFDMC results for $v_6$ models of pure
neutron matter are in reasonably good agreement with equivalent Correlated
Basis Function (CBF) calculations, providing energies per particle which are
slightly lower than the CBF ones. However, the inclusion of the spin--orbit
force leads to quite different results particularly at relatively high
densities. The resulting equation of state from AFDMC calculations is harder
than the one from previous Fermi hypernetted chain studies commonly used to
determine the neutron star structure.
