We investigate the dynamical possibility for the formation of a
transient new coherent condition of matter in high-energy hadronic
collisions. The coherent bosonic amplitude is characterized by a
non-zero momentum and is sustained by $P$-wave interactions of
quasi-pions in a dense fermionic medium. We make quantitative
estimates of several essential properties: the condensate momentum and
the fermionic density, the size of the coherent amplitude and the
negative energy density contributed by the condensate, a
characteristic proper time for the system to exist prior to breakdown
into a few pions, and a characteristic extension of the system over
the plane perpendicular to the collision axis. These quantities then
allow us to make definite estimates of new signals: a few pions with
anomalously small transverse momenta $\leq 50$ MeV/c; and a possible
anomalous bremsstrahlung of very soft photons with characteristic
transverse momenta as low as about 4 MeV/c.