A continuum nonlocal Dirac operator multiplied by an invertible zero-free entire function has exactly the same kernel and finite-momentum zero set as the ordinary Dirac operator, so fermion doubling is absent.
Asymptotic Microcausality to Macrocausality: Complete Quantum Electrody- namics and the RegulatedS-Matrix,
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An inquiry on the Absence of Fermion Doubling and why the Nielsen-Ninomiya Theorem Does Not Apply to Nonlocal Quantum Field Theory
A continuum nonlocal Dirac operator multiplied by an invertible zero-free entire function has exactly the same kernel and finite-momentum zero set as the ordinary Dirac operator, so fermion doubling is absent.