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A new class of R² type of actions without ghosts and tachyons is found in which both the vierbein field e_μᵃ and the spin connection ω_μᵃᵇ are independent and propagating fields. A complete set of spin-projection operators for e_μᵃ and ω_μᵃᵇ is constructed. The particle content of these actions and other R² theories in the literature is given. The relation of this work to the interesting work of Neville is discussed.
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Sezgin et al. (1980) studied this question.
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