'Dynamical' representation of the Poincare algebra for higher-spin fields in interaction with plane waves

To avoid the defects of higher-spin interaction theory, the field-dependent invariant representation (the 'dynamical' representation) of the Poincare algebra is considered as a dynamical principle. A general 'dynamical' repre sentation for a single elementary particle of arbitrary spin in the presenc e of a plane-wave field is constructed and the corresponding forms of the h igher-spin interaction terms found. The properties of relativistically inva riant first-order higher-spin equations with the 'dynamical' interaction ar e examined. It is shown that the Rarita-Schwinger spin-3/2 equation with th e 'dynamical' interaction is causal and free from algebraic inconsistencies , As distinct from the first-order higher-spin relativistic equations with the minimal coupling, there exist the Klein-Gordon divisors for the first-o rder equations with the non-minimal, 'dynamical' interaction, and the corre sponding Klein-Gordon equations are causal.