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We propose a prescription for making off-shell and expanding the S-matrix elements that corresponds to a non-abelian gauge invariant tachyon action with arbitrary mass $m$. We apply this proposal for the S-matrix element of four tachyons and for the S-matrix element of two tachyons and two gauge fields, in both bosonic and superstring theories. In the superstring theory, the leading terms of the expansion are in full agreement with the symmetrised trace of the direct non-abelain generalization of tachyonic Born-Infeld action in which the potential is consistent with $V(T)=e^{\pi\alpha'^2 m^2T^2}$. In the bosonic theory, the leading terms are reproduced by the above action and some other gauge invariant couplings. These extra couplings are zero in the abelian case.
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