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Abelian Anomalies in Nonlocal Regularization
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Nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the barrier to quantizing the fully gauged chiral invariant theory, and consequences.
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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.
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