Tbh I’ve taken 8 quantum field theory courses and I’m still not 100% sure what a Fermion is
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*universal cover of the Poincare group
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you mean SL(2,C) Right?
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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.
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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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The Lorentz group SO(3,1) is a symmetry group of relativistic mechanics. Quantum mechanically, the representations of this group that are interesting are those of the double cover, SL(2,C). The smallest irreducible representation of this group gives the “spin-1/2” representation.
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