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WS24/25 – Abstract
Holger Gies
(Friedrich-Schiller-Universität Jena)
12.12.2024
Quantum field theories of relativistic Luttinger fermions
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 constructed, representing first examples of high-energy complete quantum field theories based on purely fermionic matter degrees of freedom.
As examples, we investigate a class of quantum field theories with relativistic Luttinger fermions and local self-interaction in scalar channels which feature an asymptotically free high-energy regime. The long-range behavior can be addressed by mean-field theory which is exact in the limit of large flavor numbers, or by the functional renormalization group. We identify two models which undergo dimensional transmutation, interconnecting the asymptotically free high-energy regime with an ordered low-energy phase sustaining a vacuum condensate and scalar excitations on top of the condensate. We also study the analytic structure of the Luttinger-fermionic propagator in the various possible massive phases.
