This article is cited in 8 papers

Generalization of Dirac conjugation in the superalgebraic theory of spinors

V. V. Monakhov

St. Petersburg State University, St. Petersburg, Russia

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.

Keywords: second quantization, CAR algebra, Clifford algebra, Dirac matrix, spinor, Dirac conjugation, Lorentz transformation, Lorentz covariance, causality, charge operator.

PACS: 03.70.+k, 11.10.Kk, 11.30.Cp

MSC: 15A66

Received: 29.10.2018
Revised: 20.12.2018

DOI: 10.4213/tmf9650

 English version: Theoretical and Mathematical Physics, 2019, 200:1, 1026–1042

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