The fermionic double smeared null energy condition

TL;DR

This paper proves the fermionic double smeared null energy condition in 4D Minkowski space, extending previous bosonic results by addressing fermionic-specific challenges and providing explicit analytic and numerical results.

Contribution

It extends the double smeared null energy condition proof to fermionic theories, adapting existing methods to handle fermionic energy-momentum tensor complexities.

Findings

Proved DSNEC for fermions in 4D flat spacetime.

Derived explicit analytic results for massless fermions.

Provided numerical analysis of mass dependence in Gaussian smearing.

Abstract

Energy conditions are crucial for understanding why exotic phenomena such as traversable wormholes and closed timelike curves remain elusive. In this paper, we prove the Double Smeared Null Energy Condition (DSNEC) for the fermionic free theory in 4-dimensional flat Minkowski space-time, extending previous work on the same energy condition for the bosonic case [1][2] by adapting Fewster and Mistry's method [3] to the energy-momentum tensor $T_{++}$. A notable difference from previous works lies in the presence of the $\gamma_0 \gamma_+$ matrix in $T_{++}$, causing a loss of symmetry. This challenge is addressed by making use of its square-root matrix. We provide explicit analytic results for the massless case as well as numerical insights for the mass-dependence of the bound in the case of Gaussian smearing.