  We present, for the first time, an action principle that gives the equations
of motion of an extended body possessing multipole moments in an external
gravitational field, in the weak field limit. From the action, the
experimentally observable quantum phase shifts in the wavefunction of an
extended object due to the coupling of its multipole moments with the
gravitational field are obtained. Also, since the theory may be quantized using
the action, the present approach is useful in the interface between general
relativity and quantum mechanics.
