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Ok, this question looks a bit ridiculous at the outset. However, I was thinking, and I couldn't actually come up with a reason why there shouldn't exist a representation of the Lorentz group that was, say, spin-$1/4$. These wouldn't be spinors, and I don't exactly know what they would look like, but I can't find any reason to prevent them from existing.

Therefore, are such theories forbidden? If so, why? If not, can any such theory ever be physically relevant?

Qmechanic
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2 Answers2

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The Lorentz group, SO(1,3) has a universal cover that is a double cover, Spin(1,3).

This is the origin of spin-1/2.

This suggests that had we a spacetime which had a rotation group $G$ whose universal cover $UG$ was a quadruple cover then we ought to find that this theory has spin-1/4 particles.

Mozibur Ullah
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2

In 2D you can have anyons, which can have any spin.

See https://en.m.wikipedia.org/wiki/Anyon

my2cts
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