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. 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 four spacetime dimensions. In particular, new asymptotically free self-interacting field theories can be identified, representing first examples of high-energy complete quantum field theories based on purely fermionic matter degrees of freedom. As examples, we discuss models which undergo dimensional transmutation and low- energy condensate formation with scalar excitations on top of the condensate. We observe that a corresponding Yukawa model exhibits features similar to self-organized criticality with a natural separation of low-energy observables from high energy initial scales without the need for any fine-tuning. We also critically examine the analytic structure of the Luttinger-fermionic propagator in the various gapped phases and discuss possible consequences for asymptotic states.

mathematical physics

Audience: researchers in the discipline

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