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How does a state vector change under an exchange of a boson and a fermion ? That's how is $\Psi_{\alpha,\beta}$ related to $\Psi_{\beta,\alpha}$ where $\alpha$ and $\beta$ are a boson and a fermion respectively?

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A boson and a fermion are distinguishable particles so quantum statistics don't come into it. You get two orthogonal state vectors. –  Michael Brown May 16 '13 at 11:49
    
@MichaelBrown Maybe the question makes sense in the case of the supersymmetry? –  firtree May 16 '13 at 13:59
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