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Superalgebraic representation of Dirac matrices

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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.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. V. Monakhov

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  1. V. V. Monakhov
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Correspondence to V. V. Monakhov.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 186, No. 1, pp. 87–100, January, 2016.

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Monakhov, V.V. Superalgebraic representation of Dirac matrices. Theor Math Phys 186, 70–82 (2016). https://doi.org/10.1134/S0040577916010062

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