  In close analogy to fermionic many-body theory the truncation of the bosonic
BBGKY density matrix hierarchy on the two-body level leads to a coupled set of
nonlinear equations of motion for the one-body density matrix and the two-body
correlation function. These equations provide a nonperturbative description of
the nonequilibrium time evolution of particle number conserving bosonic
many-body systems including the dynamical resummation of parquet-like diagrams.
Within this framework we study the properties of a pionic system as a function
of temperature and density with focus on two-body quantities. For each
temperature we find a related pion density for which the relative strength of
the two-body correlation function assumes a maximum and the pionic system is
far from the mean-field limit. Since these correlated phases up to $T$=200 MeV
only appear at rather low pion density, the hot and dense pion gas as generated
in ultrarelativistic nucleus-nucleus collisions should be well described within
mean-field theory; i.e. the HBT analysis of pion sources from $\pi-\pi$
correlations should remain valid even in the case of strongly interacting
pions.
