Superalgebra and BRST supersymmetry 1: odd vs even It is said that most of theories, the even elements of the superalgebra correspond to bosons and odd elements to fermions (but this is not always true; for example, the BRST supersymmetry is the other way around)..

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*Why BRST supersymmetry is the other way around: odd  elements of the superalgebra correspond to bosons and even elements to fermions ?

 A: *

*It is not completely clear what the quote from the Wikipedia page (October, 2020) mentioned by OP refers to.

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*Perhaps it refers to that e.g. the Yang-Mills Grassmann-even gauge parameter $\xi^a$ in the gauge transformation $\delta A_{\mu}=D_{\mu}\xi^a$ is related to the Grassmann-odd FP ghost $c^a$ in the BRST formulation.


*Perhaps it refers to the shifted Grassmann-grading in the antibracket/Gerstenhaber algebra used in the Batalin-Vilkovisky (BV) formulation.




*Bosons and fermions are by definition$^1$ physical particles that follow Bose-Einstein and Fermi-Dirac statistics, respectively, but e.g. Faddeev-Popov (FP) ghosts (and many auxiliary fields in the BRST formulation) are not physical fields, and therefore not bosons or fermions. Instead they first and foremost carry Grassmann-parity, although they (in the Hamiltonian formulation) often satisfy a CCR/CAR.
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$^1$ In supermathematics, which deals with supernumbers, it is common to refer to Grassmann-even and Grassmann-odd variables as bosons and fermions, respectively, but it is strictly speaking a misnomer.
