6533b852fe1ef96bd12aa50d
RESEARCH PRODUCT
Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
Matthias NeubertMatthias NeubertAndré Leclairsubject
PhysicsHigh Energy Physics - TheoryNuclear and High Energy PhysicsUnitarityStrongly Correlated Electrons (cond-mat.str-el)010308 nuclear & particles physicsCritical phenomenaFOS: Physical sciencesKinetic termFermionMathematical Physics (math-ph)Lorentz covariance01 natural sciencesLorentz groupCondensed Matter - Strongly Correlated ElectronsHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)High Energy Physics - Theory (hep-th)0103 physical sciences010306 general physicsCritical exponentMathematical PhysicsMathematical physicsSymplectic geometrydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-10-05 |