Massive super-Yang-Mills quantum mechanics: Classification and the relation to supermembrane

We classify the supersymmetric mass deformations of all the super-Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super-Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.