We study the interaction of gauge fields of arbitrary half-integer spins withthe homogeneous electromagnetic field. We reduce the problem of obtaining thegauge-invariant Lagrangian and transformations of the half-integer spin fieldsin the external field to an algebraic problem of search for a set of operatorswith certain algebraical features using the representation of the higher-spinfields as vectors in a pseudo-Hilbert space. We consider such construction atlinear order in the external electromagnetic field and also present an explicitform of interaction Lagrangians and gauge transformations for the massiveparticles of spins 3/2 and 5/2 in terms of symmetric spin-tensor fields. Theobtained result is valid for space-time of arbitrary even dimension.
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