The spin-3/2 elementary particle, known as Rarita-Schwinger (RS) fermion, is described by a
vector-spinor field Psi_μ, whose number of components is larger than its independent degrees of
freedom (DOF). Thus the RS equations contain nontrivial constraints to eliminate the redundant
DOF. Consequently the standard procedure adopted in realizing relativistic spin-1/2 quasiparticle
is not capable of creating the RS fermion in condensed matter systems. In this work, we propose
a generic method to construct a Hamiltonian which implicitly contains the RS constraints, thus
includes the solutions with the eigenstates and energy dispersions being exactly the same as those
of RS equations. By implementing the proposed 16 × 16 or 6 × 6 Hamiltonian, one can realize
the 3 dimensional (3D) or 2 dimensional (2D) massive RS quasiparticles, respectively. In the non-
relativistic limit, the 2D 6×6 Hamiltonian can be reduced to two 3×3 Hamiltonians which describe
the positive and negative energy parts respectively. Due to the nontrivial constraints, this simplified
2D massive RS quasiparticle has an exotic property: it has vanishing orbital magnetic moment
while its orbital magnetization is finite. Finally, we discuss the material realization of the 2D
non-relativistic RS quasiparticle.