Since the Higgs mechanism is so intimately tied to binding together massless chiral fermions, does it happen to have anything to say about the spin statistics issue?

I'm actually assuming the answer is no, but perhaps there is a deeper tie there that I'm missing completely. So, just curious...

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    $\begingroup$ what do you meand "the spin statistics problem"? $\endgroup$ – anna v Mar 22 '13 at 4:57
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    $\begingroup$ The spin-statistics theorem was proved by Pauli long before anyone was thinking about the Higgs mechanism, so I can't see that they have anything to do with each other. The Higgs is not needed for "binding together massless chiral fermions" in general (it is needed in the standard model), but the spin-statistics theorem applies to any Lorentz invariant quantum field theory satisfying some mild technical assumptions. $\endgroup$ – Michael Brown Mar 22 '13 at 5:52

The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated.

The Higgs field gives us interactions between chiral fermions and the Higgs, $yh\cdot \chi_\alpha\eta^\alpha$ which produces mass terms $m \chi_\alpha\eta^\alpha$ if the Higgs field has a vacuum expectation value $h=v$. We have $m=yv$.

However, in more general quantum field theories, one may write down similar (bilinear) mass terms manually without any Higgs field (and without cubic Yukawa terms) and none of these issues affects the fact that the spin-statistics relationship holds. The field $h$ is spin-zero field and bosonic, the fields $\chi,\eta,\Psi$ (the latter is the 4-component Dirac spinor combining the previous two) are spin-1/2 and fermionic fields.


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