  We discuss selected aspects of classical relativistic scalar field theories
with nonzero chemical potential. First, we offer a review of classical field
theory at nonzero density within the Lagrangian formalism. The aspects covered
include the question of equivalence of descriptions of finite-density states
using a chemical potential or time-dependent field configurations, the choice
of Hamiltonian whose minimization yields the finite-density equilibrium state,
and the issue of breaking of Lorentz invariance. Second, we demonstrate how the
low-energy effective field theory for Nambu-Goldstone (NG) modes arising from
the spontaneous breakdown of global internal symmetries can be worked out
explicitly by integrating out the heavy (Higgs) fields. This makes it possible
to analyze the spectrum of NG modes and their interactions without having to
deal with mixing of NG and Higgs fields, ubiquitous in the linear-sigma-model
description of spontaneous symmetry breaking.
