Spinor and vector representations in four-dimensional Grassmann space

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Abstract
Spinor, scalar, and vector irreducible representations of generators of the Lorentz transformations in a four‐dimensional Grassmann subspace of a d‐dimensional Grassmann space are studied. For d=5 there are four spinor representations with the properties of Majorana spinors and two scalar, two three‐vector and two four‐vector representations with the properties of bosons, offering the possibility of the canonical quantization of not only bosonic but also fermionic fields.