  We describe the structure of the moduli space of $\sigma$-model couplings for
the worldsheet description of a system of $N$ D-particles, in the case that the
couplings are represented by a pair of logarithmic recoil operators. We derive
expressions for the canonical momenta conjugate to the D-particle couplings and
the Zamolodchikov metric to the first few orders in $\sigma$-model perturbation
theory. We show, using only very general properties of the operator product
expansion in logarithmic conformal field theories, that the canonical dynamics
on moduli space agree with the predictions of the non-abelian generalization of
the Born-Infeld effective action for D-particles with a symmetrized trace
structure. We demonstrate that the Zamolodchikov metric naturally encodes the
short-distance structure of spacetime, and from this we derive uncertainty
relations for the D-particle coordinates directly from the quantum string
theory. We show that the moduli space geometry naturally leads to new forms of
spacetime indeterminancies involving only spatial coordinates of target space
and illustrate the manner in which the open string interactions between
D-particles lead to a spacetime quantization. We also derive appropriate
non-abelian generalizations of the string-modified Heisenberg uncertainty
relations and the space--time uncertainty principle. The non-abelian
uncertainties exhibit decoherence effects suggesting the interplay of quantum
gravity in multiple D-particle dynamics.
