  The fermion representation for S = 1/2 spins is generalized to spins with
arbitrary magnitudes. The symmetry properties of the representation is analyzed
where we find that the particle-hole symmetry in the spinon Hilbert space of S
=1/2 fermion representation is absent for S > 1/2. As a result, different path
integral representations and mean field theories can be formulated for spin
models. In particular, we construct a Lagrangian with restored particle-hole
symmetry, and apply the corresponding mean field theory to one dimensional (1D)
S = 1 and S = 3/2 antiferromagnetic Heisenberg models, with results that agree
with Haldane's conjecture. For a S = 1 open chain, we show that Majorana
fermion edge states exist in our mean field theory. The generalization to spins
with arbitrary magnitude S is discussed. Our approach can be applied to higher
dimensional spin systems. As an example, we study the geometrically frustrated
S = 1 AFM on triangular lattice. Two spin liquids with different pairing
symmetries are discussed: the gapped px + ipy-wave spin liquid and the gapless
f-wave spin liquid. We compare our mean field result with the experiment on
NiGa2S4, which remains disordered at low temperature and was proposed to be in
a spin liquid state. Our fermionic mean field theory provide a framework to
study S > 1/2 spin liquids with fermionic spinon excitations.
