On the connection between generators of three- and four dimensional turns with Hamilton's operators for particles with spins 1 and 1/2

It is shown in the framework of the nonrelativistic theory that the structure of Hamilton operator for particles with spin 1 is strictly defined by the structure of group generator of three-dimensional turns; operator of spin, by infinitesimal operator of this groups. For particles with spin 1/2 similar connection is established with way transition from the 3-dimensional space to the Euclidean 4-dimensional space. Four-dimensional formalism allows one to construct such combinations of generator turns, which have commutational relations identical to those of orbital momentum, eiegevalues multiple to 1/2 infinitesimal operator-identical to the basis of Pauli matrix. The structure of such generator combinations corresponds to that one of Hamilton operator for Pauli equation. In 4-dimensional space the symmetry is established between equations for particles with spins 1 and 1/2. The connection of transformational properties of the wave function of spin 1/2 particle with the group of 4-dimensional space turns is also considered