On the Regularized Fermionic Projector of the Vacuum

TL;DR

This paper develops a method to construct spherically symmetric regularized fermionic projectors that satisfy specific distributional conditions, revealing a multi-layer structure near the light cone and discussing implications for Lorentz symmetry and state normalization.

Contribution

It introduces a novel regularization approach for fermionic projectors with controlled tails and analyzes their structural and symmetry properties.

Findings

Regularized fermionic projectors exhibit a multi-layer structure near the light cone.

The regularization breaks Lorentz symmetry intentionally.

Parameter freedom affects fermionic state normalization.

Abstract

We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional ${\mathcal{M}} P$-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 consequences for the normalization of the fermionic states are discussed.