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The massive Dirac fermion is strange in that it transforms under the Poincare group as a direct sum of two spin-1/2 representations of the group $(\frac{1}{2},0)\oplus (0,\frac{1}{2})$. This suggests that it is actually composed of two distinct particles, and may even be a ''bound state'' of two Weyl fermions.

To what extent can one say that the electron is a bound state of two Weyl fermions with the attractive force provided by the Higgs?

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    $\begingroup$ What is the electric charge of the Weyl fermions? $\endgroup$ Apr 17, 2019 at 20:41

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'Bound state' would not be an apropos depiction. Bounding two fermions would give rise to an effective boson.

Rather, an electron is a chameleon changing its color between two different Weyl (left-handed/right-handed) states all the time. An electron walks like a drunkard: it ziggs (left-handed) and zaggs (right-handed), constantly buffeted by the Higgs lampposts, which prevent the electron from traveling at the speed of light.

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    $\begingroup$ An electron in an energy eigenstate should not be changing in time, and would presumably be in a constant superposition of the two Weyl states rather than oscillating. $\endgroup$
    – Rococo
    Apr 17, 2019 at 21:40
  • $\begingroup$ @Rococo, heard of neutrino oscillation? If neutrino mass eigenstate is a constant superposition of different flavors, why it is talked in terms of oscillation? $\endgroup$
    – MadMax
    Apr 18, 2019 at 13:45
  • $\begingroup$ Well, a neutrino cannot typically be confined in one place, so considering stationary states is not very relevant. Not so with electrons. However, I should be careful with the above statements: see physics.stackexchange.com/questions/407788/… and physics.stackexchange.com/questions/246637/… for more information on the difference between the chirality of a field (which makes sense) and the chirality of a single particle state of that field (which may not). $\endgroup$
    – Rococo
    Apr 18, 2019 at 16:12

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