Abstract
We give a proof of the most general multiple-scalar field theory in a flat space-time free of Ostrogradski ghosts. We start from the assumption that the action is a functional of the scalar fields with up to second-order derivatives (which in general can have field equations with up to fourth-order derivatives), and arrive at the most general field theory that can be constructed such that the field equations have up to second-order derivatives. Naturally, this theory includes all physically viable multi-scalar field theories in flat space-time, in the sense that they do not suffer from the Ostrogradski instability [M. Ostrogradsky, Memoires de lAcademie Imperiale des Science de Saint-Petersbourg 4, 385 (1850)].
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