Non-Hermitian Lagrangian for quasi-relativistic fermions

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.

9 pages, comments added

References in corpus (5)

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• Critical behavior of the PT-symmetric $i{\varphi }^3$ quantum field theory
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