  New equations describing particles with spin 3/2 are derived. The non-local
equation with the unique mass can be considered as "square root" of the Proca
equation in the same sense as the Dirac equation is related to the
Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles
with three mass states. The equations considered involve fields with spin-3/2
and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting
states with definite energy, spin, and spin projections are obtained. All
independent solutions of the local equation are expressed through projection
matrices. The first order relativistic wave equation in the 20-dimensional
matrix form, the relativistically invariant bilinear form and the corresponding
Lagrangian are given. Two parameters characterizing non-minimal electromagnetic
interactions of fermions are introduced, and the quantum-mechanical Hamiltonian
is found. It is proved that there is only causal propagation of waves in the
approach considered.
