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Expanding @ACuriousMind comment as an answer: By the Spin-Statistics Theorem the symmetry group of Lorentz-Invariant QFT is the lorentz group $SO^+(1,3)$ of which $SL_2(C)$ is the universal covering group. The irreducible representations of the symmetry group of the theory, are related naturaly to the way the wavefunction changes under exchange of the ...

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