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

Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models