Recently, we have constructed an action for the dynamical
system of N nearly coincident multiple D0-branes and strings
connecting these D0-branes (referred to as the mD0 system). This
action includes an arbitrary positive definite function M(H) of the
relative motion Hamiltonian H and possesses all the properties
expected from a multiple D0-brane system of String theory for any
choice of this function. Furthermore, the 10D mD0 model, characterized
by a specific form of M(H), can be derived through dimensional
reduction from the action of the D=11 multiple M-wave (mM0) system.
The quantization of this action should result in an interesting
supersymmetric field theory in (super)space with non-commuting and
non-anticommuting coordinates, which can provide important insights
into the study of String theory.
This talk serves as a progress report on these developments: Beginning
from describing the 10D system and its properties in Lagrangian
approach, we construct the Hamiltonian formalism and discuss the
covariant quantization of its simplest three dimensional counterpart
as a preliminary step to attack the quantization of the 10D mD0-brane
system.