Symmetries of the complex Dirac-Kähler equation

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作者
I. Yu. Krivsky
R. R. Lompay
V. M. Simulik
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[1] Ukrainian Academy of Sciences,Institute for Electron Physics
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Dirac-Kähler equation; complexification; fermions; bosons; symmetries;
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摘要
We consider a complex version of a Dirac-Kähler-type equation, the eight-component complex Dirac-Kähler equation with a nonvanishing mass, which can be decomposed into two Dirac equations by only a nonunitary transformation. We also write an analogue of the complex Dirac-Kähler equation in five dimensions. We show that the complex Dirac-Kähler equation is a special case of a Bhabha-type equation and prove that this equation is invariant under the algebra of purely matrix transformations of the Pauli-Gürsey type and under two different representations of the Poincaré group, the fermionic (for a two-fermion system) and bosonic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{P}$$ \end{document}-representations. The complex Dirac-Kähler equation is also written in a manifestly covariant bosonic form as an equation for the system (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{B}$$ \end{document}μν, Φ, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{V}$$ \end{document}μ) of irreducible self-dual tensor, scalar, and vector fields. We illustrate the relation between the complex Dirac-Kähler equation and the known 16-component Dirac-Kähler equation.
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页码:541 / 558
页数:17
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