A related Wikipedia page provided a little overview. However, here's the question: If an anti-particle acquire a negative mass $m$ in QFT, doesn't $F=ma$ indicate that the anti-particle will accelerate in the opposite direction of the acting force? Why the Newtonian gravity law does not work for antimatter as mentioned in the Wikipedia webpage? What exactly is the nature of a negative mass?

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    $\begingroup$ Instead of just referencing a wiki page, could you please state your arguments. Nobody wants to read the full wiki page just to help you. Especially when the second sentence reads "... the consensus among physicists is that gravity will attract both matter and antimatter at the same rate that matter attracts matter". $\endgroup$ – Semoi Dec 6 '19 at 20:04
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    $\begingroup$ There is a misconception about mass $m$ in QFT. $m$ is actually short for $|m|$. For both boson and fermion the physical mass is defined by the pole mass $p^2 - m^2 =0$, so that the sign of the mass does not matter. $\endgroup$ – MadMax Dec 6 '19 at 21:36
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    $\begingroup$ Take Dirac equation for example. For any solution of $\psi_0$ satisfying the Dirac equation with positive mass $i\not D \psi - m \psi = 0$, you can have a wave function $e^{i\gamma_5\pi/2}\psi_0$ satisfying a Dirac equation with negative mass $i\not D \psi - (-m) \psi= 0$. The difference is only a non-physical phase. $\endgroup$ – MadMax Dec 6 '19 at 21:42
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    $\begingroup$ Therefore the correct Newton equation is $F = |m|a$. The sign of mass has no meaning and does not affect any physics. $\endgroup$ – MadMax Dec 6 '19 at 21:43
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    $\begingroup$ I want to give this link for experiment running at CERN to test the behavior of antiprotons to gravity home.cern/news/news/experiments/… . $\endgroup$ – anna v Dec 7 '19 at 6:58

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