  Noncommutative field theory on Yang's quantized space-time algebra (YSTA) is
studied. It gives a theoretical framework to reformulate the matrix model as
quantum mechanics of $D_0$ branes in a Lorentz-covariant form. The so-called
kinetic term ($\sim {\hat{P_i}}^2)$ and potential term ($\sim
{[\hat{X_i},\hat{X_j}]}^2)$ of $D_0$ branes in the matrix model are described
now in terms of Casimir operator of $SO(D,1)$, a subalgebra of the primary
algebra $SO(D+1,1)$ which underlies YSTA with two contraction- parameters,
$\lambda$ and $R$. $D$-dimensional noncommutative space-time and momentum
operators $\hat{X_\mu}$ and $\hat{P_\mu}$ in YSTA show a distinctive spectral
structure, that is, space-components $\hat{X_i}$ and $\hat{P_i}$ have discrete
eigenvalues, and time-components $\hat{X_0}$ and $\hat{P_0}$ continuous
eigenvalues, consistently with Lorentz-covariance. According to the method of
Lorentz-covariant Moyal star product proper to YSTA, the field equation of
$D_0$ brane on YSTA is derived in a nontrivial form beyond simple Klein-Gordon
equation, which reflects the noncommutative space-time structure of YSTA.
