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We consider massive half-integer higher spin fields coupled to an externalconstant electromagnetic field in flat space of an arbitrary dimension andconstruct a gauge invariant Lagrangian in the linear approximation in theexternal field. A procedure for finding the gauge-invariant Lagrangians isbased on the BRST construction where no off-shell constraints on the fields andon the gauge parameters are imposed from the very beginning. As an example ofthe general procedure, we derive a gauge invariant Lagrangian for a massivefermionic field with spin 3/2 which contains a set of auxiliary fields andgauge symmetries.

Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background