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Supersymmetry is a model based on symmetry between bosons and fermions. Bosons carry force and they are described by potentials. Fermions are matter particle and they are described by wavefunctions. Does fermions carry force similary to bosons in supersymmetry? Can fermions be described by potentials instead wavefuctions?

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  • $\begingroup$ "Bosons carry force and they are described by potentials. Fermions are matter particle and they are described by wavefunctions." This is not strictly true in relativistic quantum field theory, the domain of the Standard Model of particle physics, and the SUSY extension to it. In QFT both fermions and bosons are represented by fields that interact via certain rules. But yes, in the MSSM (minimal supersymmetric standard model) you have fermionic partners to the normal force carrier bosons. $\endgroup$ Sep 30, 2023 at 21:59
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    $\begingroup$ We wouldn't usually call the exchange of a single fermion a "force", because a fermion carries half-integer spin, so it has to change the identities of the matter particles absorbing and emitting it -- which seems less like a force and more like a reaction. But if you exchange two fermions at once then you can let the matter particles keep their identities and describe the interaction with a potential. For example, there's the two-neutrino exchange force which yields a long-range $1/r^5$ potential, though it's unfortunately too small to be measured. $\endgroup$
    – knzhou
    Sep 30, 2023 at 22:01

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