Abstract. We show how, for all dimensions and signatures, a symmetry operator for the massless Dirac equation can be constructed from a conformal Killing-Yano tensor of arbitrary degree.

The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system J. Math. Phys. 53, 083703 (2012) ECE-imaging of the H-mode pedestal (invited) Rev. Sci. Instrum. 83, 10E329 (2012) The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories J. Math. Phys. 53, 072903 (2012) Operator extensions theory model for electromagnetic field-electron interaction By using conformal Killing-Yano tensors, and their generalizations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing-Yano tensors, symmetry operators that map any solution to another.

We show how, for all dimensions and signatures, the most general first-order linear symmetry operator for the massive Dirac equation is given in terms of Killing-Yano tensors. In the massless case the Killing-Yano condition is relaxed to the conformal Killing-Yano generalisation.

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The classical Kahler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.