SPINOR AND VECTOR REPRESENTATIONS IN 4-DIMENSIONAL GRASSMANN SPACE

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.