Abstract
We study the regular representation ρζ of the single-fermion algebra [Formula: see text], i.e., c2 = c+2 = 0, cc+ + c+c = ζ1, for ζ ∈ [0,1]. We show that ρ0 is a four-dimensional nonunitary representation of [Formula: see text] which is faithfully irreducible (it does not admit a proper faithful subrepresentation). Moreover, ρ0 is the minimal faithfully irreducible representation of [Formula: see text] in the sense that every faithful representation of [Formula: see text] has a subrepresentation that is equivalent to ρ0. We therefore identify a classical fermion with ρ0 and view its quantization as the deformation: ζ : 0 → 1 of ρζ. The latter has the effect of mapping ρ0 into the four-dimensional, unitary, (faithfully) reducible representation ρ1 of [Formula: see text] that is reminiscent of a Dirac fermion.
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