Sakata-Taketani spin-0 theory with external field interactions: Lagrangian formalism and causal properties

Abstract

To illustrate that a relativistic field theory need not be manifestly covariant, we construct Lorentz-invariant Lagrangian densities that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing our results to higher spin theories involving only the essential 2(2 J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.