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Recently, Paczos et al. (2308.00450) proposed a covariant quantum field theory for free and interacting tachyon fields. We show that the proposed Feynman propagator is not Lorentz invariant, proper asymptotic (in/out) tachyon states do not exist, and the proposed S-matrix describing interactions of tachyons and subluminal matter is ill-defined. Since tachyons behave as bosons, interacting tachyons may also self-interact, e.g., any interaction with ordinary matter generates such terms. As a result, the physical vacuum, instead of being at the origin of the potential, may correspond to the proper minimum of the tachyon potential, or such state does not exist at all. Our analysis indicates that quantum tachyon field does not describe a physical on-shell particle with negative mass squared.
Krzysztof Jodłowski (Thu,) studied this question.