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The new relativistic equations of motion for the particles with spin s=1,s=3/2, s=2 and nonzero mass have been introduced. The description of therelativistic canonical quantum mechanics of the arbitrary mass and spin hasbeen given. The link between the relativistic canonical quantum mechanics ofthe arbitrary spin and the covariant local field theory has been found. Themanifestly covariant field equations that follow from the quantum mechanicalequations, have been considered. The covariant local field theory equations forspin s=(1,1) particle-antiparticle doublet, spin s=(1,0,1,0)particle-antiparticle multiplet, spin s=(3/2,3/2) particle-antiparticledoublet, spin s=(2,2) particle-antiparticle doublet, spin s=(2,0,2,0)particle-antiparticle multiplet and spin s=(2,1,2,1) particle-antiparticlemultiplet have been introduced. The Maxwell-like equations for the boson withspin s=1 and $m>0$ have been introduced as well.

Covariant local field theory equations following from the relativistic canonical quantum mechanics of arbitrary spin