Euclidean Path Integral, D0-Branes and Schwarzschild Black Holes in Matrix Theory

The partition function in Matrix theory is constructed by Euclidean path integral method. The D0-branes, which move around in the finite region with a typical size of Schwarzschild radius, are chosen as the background. The mass and entropy of the system obtained from the partition function contain the parameters of the background. After averaging the mass and entropy over the parameters, we find that they match the properties of 11D Schwarzschild black holes. The period $\b$ of Euclidean time can be identified with the reciprocal of the boosted Hawking temperature. The entropy $S$ is shown to be proportional to the number $N$ of Matrix theory partons, which is a consequence of the D0-brane background.