Covariant quantum field theory of tachyons is unphysical

Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This may have changed with the recent works of Dragan et al. [J. Paczos et al., Covariant quantum field theory of tachyons, Phys. Rev. D 110, 015006 (2024); A. Dragan and A. Ekert, Quantum principle of relativity, New J. Phys. 22, 033038 (2020); A. Dragan and A. EkertNew J. Phys.25, 088002(A) (2023); A. Dragan, K. D\ifmmode \mbox{\k{e}}\else \k{e}\fi{}bski, S. Charzy\ifmmode \acute{n}\else \'{n}\fi{}ski, K. Turzy\ifmmode \acute{n}\else \'{n}\fi{}ski, and A. Ekert, Relativity of superluminal observers in $1+3$ spacetime, Classical Quantum Gravity 40, 025013 (2023); J. Paczos, S. Cedrowski, K. Turzy\ifmmode \acute{n}\else \'{n}\fi{}ski, and A. Dragan, Higgs field as a source of tachyons, arXiv:2407.06640], who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM) because they require introducing nondeterminism and wavelike behavior at the fundamental level. Unfortunately, we show that the tachyon quantum field theory proposed as a part of this program is not quantum since the tachyon field commutes at all points and the canonical commutations relations of a quantum scalar field are not satisfied. We also discuss other authors' theories, e.g., we show that the Dhar-Sudarshan's formula for the Feynman propagator violates unitarity, and we apply the Lehmann--Symanzik--Zimmermann (LSZ) formalism to tachyons for the first time, where we find that one cannot prove the LSZ asymptotic condition just by replacing plane waves with wave packets.