This article is cited in 8 papers

Superalgebraic representation of Dirac matrices

V. V. Monakhov

Saint Petersburg State University, Saint Petersburg, Russia

Abstract: 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, Dirac matrix, spinor, superspace, supersymmetry.

DOI: 10.4213/tmf8979

 English version: Theoretical and Mathematical Physics, 2016, 186:1, 70–82

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