  We borrow the minisuperspace approximation from Quantum Cosmology and the
quenching approximation from QCD in order to derive a new form of the bosonic
p-brane propagator. In this new approximation we obtain an exact description of
both the collective mode deformation of the brane and the center of mass
dynamics in the target spacetime. The collective mode dynamics is a
generalization of string dynamics in terms of area variables. The final result
is that the evolution of a p-brane in the quenched-minisuperspace approximation
is formally equivalent to the effective motion of a particle in a spacetime
where points as well as hypersurfaces are considered on the same footing as
fundamental geometrical objects. This geometric equivalence leads us to define
a new tension-shell condition that is a direct extension of the Klein-Gordon
condition for material particles to the case of a physical p-brane.
