SakataTaketani spin0 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 Lorentzinvariant Lagrangian densities that yield the equation satisfied by an interacting (twocomponent) SakataTaketani spin0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric secondrank tensor, and a symmetric secondrank tensor, with the results specialized to electromagnetic interactions. For either of the two secondrank 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 DuffinKemmerPetiau spin0 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.
 Publication:

Annals of Physics
 Pub Date:
 April 1977
 DOI:
 10.1016/00034916(77)903384
 Bibcode:
 1977AnPhy.104..427G
 Keywords:

 Electromagnetic Interactions;
 Field Theory (Physics);
 Lagrange Coordinates;
 Particle Spin;
 Relativity;
 Lorentz Transformations;
 Theoretical Physics;
 Wave Propagation;
 Nuclear and HighEnergy Physics