Quantum field theories of relativistic Luttinger fermions

Abstract

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 nonabelian 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.

5+7 pages, 1 figure, v2: additional clarifications, references added, matches version published in Physical Review D

References in corpus (23)

• Exact evolution equation for the effective potential
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• The Lee-Wick Standard Model
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Asymptotic safety: a simple example
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Ising and Gross-Neveu model in next-to-leading order
• Multi-meson Yukawa interactions at criticality
• The Ostrogradsky instability can be overcome by quantum physics
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Classical and Quantum Dynamics of Higher-Derivative Systems
• On avoiding Ostrogradski instabilities within Asymptotic Safety
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields
• Global surpluses of spin-base invariant fermions
• Is negative kinetic energy meta-stable?
• Predicting the singlet vector channel in a partially Higgsed gauge theory
• Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism
• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Boosted dark matter from a phantom fluid

Cited by in corpus (3)

• Foundations of ghost stability
• Relativistic electrodynamics with a universal length scale
• Mean-field theory for self-interacting relativistic Luttinger fermions