Abstract
The most general linear Lagrangian for massless and massive tensor fields without ghosts and tachyons is determined. Transversality is used to eliminate massless ghosts. The linear Einstein and Fierz-Pauli Lagrangians are unique for massless and massive tensor fields containing spin two. Hence, for gravitation, as for electromagnetism, gauge invariance and locality follow from positivity of the free-field energy. Symmetric and antisymmetric tensor theories with continuous zero-mass limit are found, but contain only spin one and spin zero.
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