Non-Hermitian Lagrangian for quasi-relativistic fermions

TL;DR

This paper introduces a novel Lorentz-violating fermionic Lagrangian that maintains relativistic dispersion in IR and UV regimes but not in between, challenging traditional Hermiticity and locality assumptions.

Contribution

It proposes a local, non-Hermitian Lagrangian with a Hermitian, non-local Hamiltonian, demonstrating a consistent model with relativistic dispersion in all regimes.

Findings

The model exhibits relativistic dispersion in IR and UV regimes.

The Lagrangian is local but not Hermitian, while the Hamiltonian is Hermitian but not local.

The model's consistency is validated through properties analogous to the Dirac Lagrangian.

Abstract

We present a Lorentz-symmetry violating Lagrangian for free fermions, which is local but not Hermitian, whereas the corresponding Hamiltonian is Hermitian but not local. A specific feature of the model is that the dispersion relation is relativistic in both the IR and in the UV, but not in an intermediate regime, set by a given mass scale. The consistency of the model is shown by the study of properties expected in analogy with the Dirac Lagrangian.