If you construct a fermionic Fock state(adsbygoogle = window.adsbygoogle || []).push({});

|psi> = a|psi1> + b|psi2>

where |psi1> is a 1-particle state and |psi2> is a 2-particle state, and you apply a full 2pi spatial rotation to it, then each particle contributes a factor of -1 to the amplitude because of the half-integer spin SO(3) representation it comes with.

R(2pi) |psi> = -a|psi1> + (-1)(-1)b|psi2> = -a|psi1> + b|psi2>

Now this state is not equivalent to the one we started with because the relative phase has changed. But because the 2pi rotation is an exact symmetry for the physical state the usual argument is that this coherent superposition should not be possible. That's the argument used in fermion-boson (univalent) superselection. The usual solution is to say that the different spin states are in different superselection sectors, and there are no physically constructible observables that can determine the relative phase, so that we can as well mix them incoherently.

So is it commonly accepted that the fermionic particle space separates into two superselection sectors of odd and even particle numbers? If not, why not?

In case I've made a silly mistake in my argument please forgive me. I didn't get a lot of sleep recently.

Thanks,

Jazz

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# Fermionic Fock space superselected?

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