Is it possible to extend the standard model with super positioned particles: bosons+fermions at the same time.

Instead of 2 dual particles as SUSY suggests, a particle collapses to its supercharge after measurement.

I am not sure how this idea can be extended with respect to the commutation and anti commutation relations.

The fact we see only electron in nature can be justified by saying that the probability to find a super-electron $\propto e^{-t/\tau}$

PS: I am sorry if it's a mishmash of orthogonal ideas and theories.

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    $\begingroup$ It's unclear how anything could be a boson and fermion at the same time, since the properties "its creation/annihilation operators commute" and "its creation/annihilation operator anti-commute" are mutually exclusive. $\endgroup$ – ACuriousMind Oct 9 '17 at 11:10
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    $\begingroup$ The linear combination $|b\rangle+|f\rangle$, although mathematically well-defined, is forbidden by a super-selection rule. $\endgroup$ – AccidentalFourierTransform Oct 9 '17 at 15:56
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    $\begingroup$ I'm not sure this should have been closed. Both ACuriousMind an AccidentalFourierTransform have posted comments that would be perfectly good answers, so I suggest the question should be reopened so a proper answer can be posted. $\endgroup$ – John Rennie Oct 10 '17 at 6:20

As said in the comments, in the acceptable commutation and anti commutation relations of fermions and bosons, it's impossible to create a mathematical structure that will satisfies both the bosons commutation and fermions anticommutation relations, because they are mutually exclusive.

Another way to look at it is as suggested in the comments: it's is forbidden by superselection rules, because it's impossible to change the superselection rules by any measurement/operator.

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