Noncausal propagation in spin-0 theories with external field interactions

Abstract

The two-component Sakata-Taketani (ST) spin-0 theory and the single-component Klein-Gordon theory are obtained from the five-component Duffin-Kemmer-Petiau (DKP) theory with six types of external field interactions by means of a Peirce decomposition. Whereas the DKP equation manifests the covariance, the ST equation manifests the causal properties. In particular, the presence of noncausal wave propagation when there is coupling to a second-rank tensor field is apparent from the form of the ST equation, in which the coefficients of all the space derivatives depend on the external field. Our results indicate that the causal properties of higher-spin equations should also be obvious when they are expressed in 2($2J+1\mathrm{}$)-component Schrödinger form.