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We show that the total energy in supergravity theory is nonnegative. The derivation is based on the fact that for bounded systems the Hamiltonian operator is the square of the spinor supercharge just as for globally supersymmetric systems. The result holds for any of the pure, matter-coupled, or extended versions of supergravity, except those with cosmological term for which the concept of total energy does not exist.
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Deser et al. (1977) studied this question.
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