Hybrid Dirac Fields

Hybrid Dirac fields are fields that are general superpositions of the annihilation and creation parts of four Dirac spin 1/2 fields, $\psi^{(\pm)}(x;\pm m)$, whose annihilation and creation parts obey the Dirac equation with mass $m$ and mass $-m$. We discuss a specific case of such fields, which has been called ``homeotic.'' We show for this case, as is true in general for hybrid Dirac fields (except the ordinary fields whose annihilation and creation parts both obey one or the other Dirac equation), that (1) any interacting theory violates both Lorentz covariance and causality, (2) the discrete transformations $\mathcal{C}$, and $\mathcal{CPT}$ map the pair $\psi_h(x)$ and $\bar{\psi}_h(x)$ into fields that are not linear combinations of this pair, and (3) the chiral projections of $\psi_h(x)$ are sums of the usual Dirac fields with masses $m$ and $-m$; on these chiral projections $\mathcal{C}$, and $\mathcal{CPT}$ are defined in the usual way, their interactions do not violate $\mathcal{CPT}$, and interactions of chiral projections are Lorentz covariant and causal. In short, the main claims concerning ``homeotic'' fields are incorrect.