# How can we have spinless fermions?

I've read that the Jordan-Wigner transformation changes qubits into spinless fermions. What, exactly, are spinless fermions? I'm guessing it doesn't mean spin zero which would be a boson, so what does it mean?

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It is only in relativistic quantum field theory that spin and statistics are connected; see http://en.wikipedia.org/wiki/Spin-statistics_theorem

In non-relativistic QFT the two are completely distinct. Spin manifests as local degrees of freedom, and statistics is encoded in the (anti-)commutation relations at equal times.

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Plea for help: does anyone have a self-contained (online) reference to CCR and CAR? The Wikipedia page on this is needlessly pedantic for a beginner (i.e. considering the exponentiated forms to make them compact --- I doubt the OP much cares for compactness). –  genneth Oct 11 '11 at 13:18
Thanks @genneth, so does that mean spinless does mean spin zero? –  Calvin Oct 11 '11 at 15:58
You can treat it as spin zero, but only if you don't take that to mean anything more than just a lack of local degrees if freedom. For instance, it says nothing about angular momentum. –  genneth Oct 11 '11 at 18:02