Relativistic wave equations and Lagrangian formalism for particles of arbitrary spin

Relativistic wave equations are obtained that describe a particle of arbitrary spin and parity and do not contain additional conditions. The fields that satisfy these equations transform in accordance with finite-dimensional reducible representations of the Lorentz group and contain principal and auxiliary components. The fields contain the least possible number of components. On the basis of these equations a Lagrangian formalism is set up and one can investigate different types of interaction. As an example, the interaction of a particle with arbitrary spin with the electromagnetic field is considered. For this case the Feynman rules are written down.