Symmetries of the complex Dirac-K�hler equation

Abstract

We consider a complex version of a Dirac-Kahler-type equation, the eight-component complex Dirac-Kahler 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-Kahler equation in five dimensions. We show that the complex Dirac-Kahler 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-Gursey type and under two different representations of the Poincare group, the fermionic (for a two-fermion system) and bosonic $$\mathcal{P}$$ -representations. The complex Dirac-Kahler equation is also written in a manifestly covariant bosonic form as an equation for the system ( $$\mathcal{B}$$ μν, Φ, $$\mathcal{V}$$ μ) of irreducible self-dual tensor, scalar, and vector fields. We illustrate the relation between the complex Dirac-Kahler equation and the known 16-component Dirac-Kahler equation.