Quantum field theories of relativistic Luttinger fermions
Holger Gies (Helmholtz-Institut Jena, Fröbelstieg 3, D-07743 Jena, Germany, Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich Schiller University Jena, Max Wien Platz 1, 07743 Jena, Germany, GSI Helmholtzzentrum für Schwerionenforschung, Planckstr. 1, 64291 Darmstadt, Germany); Philip Heinzel (Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich Schiller University Jena, Max Wien Platz 1, 07743 Jena, Germany); Johannes Laufkötter (Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich Schiller University Jena, Max Wien Platz 1, 07743 Jena, Germany); Marta Picciau (Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich Schiller University Jena, Max Wien Platz 1, 07743 Jena, Germany)
We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. Gauge theories with relativistic Luttinger fermions exhibit a strong paramagnetic dominance, requiring large non-Abelian gauge groups to maintain asymptotic freedom. We comment on the possibility to use Luttinger fermions for particle physics model building and the expected naturalness properties of such models.
