  We study a model of N-component complex fermions with a kinetic term that is
second order in derivatives. This symplectic fermion model has an Sp(2N)
symmetry, which for any N contains an SO(3) subgroup that can be identified
with rotational spin of spin-1/2 particles. Since the spin-1/2 representation
is not promoted to a representation of the Lorentz group, the model is not
fully Lorentz invariant, although it has a relativistic dispersion relation.
The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a
unitary time evolution. Renormalization-group analysis shows the model has a
low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed
points. The critical exponents are computed to two-loop order. Possible
applications to condensed matter physics in 3 space-time dimensions are
discussed.
