Tbh I’ve taken 8 quantum field theory courses and I’m still not 100% sure what a Fermion is
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Also this is the definition of spin-1/2 which, outside of four dimensions, isn’t equivalent to “Fermion.” For example, in 1+1 dimensions, the Lorentz group is simply connected and there is no spin-1/2 representation.
indeed there are only so many dimensions in which you can have chiral fermions .. i believe you can only satisfy the Clifford algebra every other 4 dimensions if i'm recalling correctly
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Clifford algebras have representations in all dimensions greater than 2, and there’s a pretty systematic way of constructing them.
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i think i must be thinking about chiral fermions then
End of conversation
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