Geodesic
Superalgebraic representation of Dirac matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 87-100

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We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.
Keywords: Grassmann algebra, Clifford algebra, quantum field theory, generalized matrix algebra, spinor, superspace, supersymmetry.
Mots-clés : Dirac matrix 
@article{TMF_2016_186_1_a4,
     author = {V. V. Monakhov},
     title = {Superalgebraic representation of {Dirac} matrices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {87--100},
     publisher = {mathdoc},
     volume = {186},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a4/}
}
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V. V. Monakhov. Superalgebraic representation of Dirac matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 87-100. http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a4/