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As a step toward clarification of the power of supersymmetry (SUSY) in Matrixtheory, a complete calculation, including all the spin effects, is performed ofthe effective action of a probe D-particle, moving along an arbitrarytrajectory in interaction with a large number of coincident source D-particles,at one loop at order 4 in the derivative expansion. Furthermore, exploiting theSUSY Ward identity developed previously, the quantum-corrected effectivesupersymmetry transformation laws are obtained explicitly to the relevant orderand are used to verify the SUSY-invariance of the effective action. Assumingthat the agreement with 11-dimensional supergravity persists, our result can beregarded as a prediction for supergravity calculation, which, yet unavailable,is known to be highly non-trivial.Comment: 27 page

Fully off-shell effective action and its supersymmetry in matrix theory