We present a field theoretical equation of state for nuclear matter an
d neutron-rich matter in beta equilibrium using the chiral sigma model
. The model includes an isoscalar vector field generated dynamically a
nd reproduces the empirical values of the nuclear matter saturation de
nsity and binding energy and the isospin symmetry coefficient for asym
metric nuclear matter. The energy per nucleon of nuclear matter as pre
dicted by our calculation is in very good agreement, up to about a den
sity of 4n(s) (n(s) = nucleon number density for saturating nuclear ma
tter), with the estimates inferred from heavy-ion collision data. An a
strophysical application, relating to neutron star structure, is prese
nted. An extension of the nuclear matter equation of state for finite
temperatures (up to 15 MeV) is given, and the phase transition to (u,
d, s) quark matter is discussed.