fractional statistics that can cannot occur in three-dimensional space

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GoodTaste

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Here we witness a peculiar description of "can can't occur" - whether it can occur or can't occur, you decide.

The source Nature is one of the most prestigious journals of science on this planet. What is interesting is the psychology behind this "can can't occur" phenomenon.

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Anyons are even more unique. All elementary particles fall into one of two possible types — fermions and bosons. Anyons are neither. The defining property of fermions (which include electrons) is Fermi statistics: when two identical fermions switch spatial positions, their quantum-mechanical wave — the wave function — is rotated by 180 degrees. When bosons exchange places, their wave doesn’t change. Switching two anyons should produce a rotation by some intermediate angle, an effect called fractional statistics that can cannot occur in three-dimensional space but only as collective states of electrons confined to move in two dimensions.


Source: Nature 03 JULY 2020
https://www.nature.com/articles/d41586-020-01988-0
 
It's a typo.
 
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