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

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

2007-05-31

arxiv.org/abs/0705.4657v2

JHEP 0710:027,2007

Physics

High Energy Physics

High Energy Physics - Theory

v2: Published version, minor typose corrected

Scientific paper

10.1088/1126-6708/2007/10/027

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.

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