We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional M P-product. The method is to analyze regularization tails with a power-law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multi-layer structure of the fermionic projector near the light cone. The remaining freedom for the regularization parameters and the

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... onsequences for the normalization of the fermionic states are discussed.