  We discuss collective coordinate quantization of the half-BPS geometries of
Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized
by a single function $u$ on a plane. We treat this function as a collective
coordinate. We arrive at the collective coordinate action as well as path
integral measure by considering D3 branes in an arbitrary LLM geometry. The
resulting functional integral is shown, using known methods (hep-th/9309028),
to be the classical limit of a functional integral for free fermions in a
harmonic oscillator. The function $u$ gets identified with the classical limit
of the Wigner phase space distribution of the fermion theory which satisfies u
* u = u. The calculation shows how configuration space of supergravity becomes
a phase space (hence noncommutative) in the half-BPS sector. Our method sheds
new light on counting supersymmetric configurations in supergravity.
