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Generalization of Dirac Conjugation in the Superalgebraic Theory of Spinors

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Abstract

In the superalgebraic representation of spinors using Grassmann densities and the corresponding derivatives, we introduce a generalization of Dirac conjugation, and this generalization yields Lorentz-covariant transformations of conjugate spinors. The signature of the generalized gamma matrices, the number of them, and the decomposition of second quantization with respect to momenta are given by a variant of the generalized Dirac conjugation and by the requirement that the algebra of canonical anticommutation relations should be preserved under transformations of spinors and conjugate spinors.

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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.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 1, pp. 118–136, July, 2019.

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Monakhov, V.V. Generalization of Dirac Conjugation in the Superalgebraic Theory of Spinors. Theor Math Phys 200, 1026–1042 (2019). https://doi.org/10.1134/S0040577919070079

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