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"Dynamical” representation of the Poincaré algebra for higher-spin fields in interaction with plane waves. (English) Zbl 0930.35150

Summary: To avoid the defects of higher-spin interaction theory, the field-dependent invariant representation (the ‘dynamical’ representation) of the Poincaré algebra is considered as a dynamical principle. A general ‘dynamical’ representation for a single elementary particle of arbitrary spin in the presence of a plane-wave field is constructed and the corresponding forms of the higher-spin interaction terms are found. The properties of relativistically invariant first-order higher-spin equations with the ‘dynamical’ interaction are examined.

It is shown that the Rarita-Schwinger spin-$\frac{2}{2}$ equation with the ‘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-order equations with the non-minimal, ‘dynamical’ interaction, and the corresponding Klein-Gordon equations are causal.

##### MSC:
 35Q40 PDEs in connection with quantum mechanics 81R05 Representations of finite-dimensional groups and algebras in quantum theory