Abstract: We study the Hamiltonian
group of a symplectic manifold, satisfying some mild
additional assumptions, by means of the associated quantomorphism
group. Recall that, according to Souriau, the quantomorphism group is the strict
contactomorphism group of the total space of
a prequantization bundle over the manifold in
question. Our investigations are concentrated on the problem of estimations (from
below) of the Hofer metric on the Hamiltonian group. We establish the
unboundedness of the metric and its non-degeneracy using contact geometry instead
of hard symplectic methods known from the literature.