  In this work we consider the effects of gravitons and their fluctuations on
the dynamics of two masses using the Feynman-Vernon influence functional
formalism, applied to nonequilibrium quantum field theory and semiclassical
stochastic gravity earlier by Calzetta, Hu and Verdaguer [1-3], and most
recently, to this problem by Parikh, Wilczek and Zahariade [4-6]. The Hadamard
function of the gravitons yields the noise kernel acting as a stochastic
tensorial force in a Langevin equation governing the motion of the separation
of the two masses. The fluctuations of the separation due to the graviton noise
are then solved for various quantum states including the Minkowski vacuum,
thermal, coherent and squeezed states. The previous considerations of Parikh et
al. are only for some selected modes of the graviton, while in this work we
have included all graviton modes and polarizations. We comment on the
possibility of detecting these fluctuations in primordial gravitons using
interferometors with long baselines in deep space experiments.
