  We study properties of entangled systems in the (mainly non-relativistic)
second quantization formalism. This is then applied to interacting and
non-interacting bosons and fermions and the differences between the two are
discussed. We present a general formalism to show how entanglement changes with
the change of modes of the system. This is illustrated with examples such as
the Bose condensation and the Unruh effect. It is then shown that a
non-interacting collection of fermions at zero temperature can be entangled in
spin providing that their distances do not exceed the inverse Fermi wavenumber.
Beyond this distance all bipartite entanglement vanishes, although classical
correlations still persist. We compute the entanglement of formation as well as
the mutual information for two spin-correlated electrons as a function of their
distance. The analogous non-interacting collection of bosons displays no
entanglement in the internal degrees of freedom. We show how to generalize our
analysis of the entanglement in the internal degrees of freedom to an arbitrary
number of particles.
