Enhanced Negative Energy with a Massless Dirac Field

TL;DR

This paper investigates the limits of negative energy density carried by a massless Dirac field in a slab, finding that arbitrarily large negative energy densities are possible in higher dimensions, relevant for wormhole physics.

Contribution

It demonstrates that states with arbitrarily large negative energy density can exist for massless Dirac fields in 3+1 dimensions, extending previous vacuum state analyses.

Findings

States with enhanced negative energy exist above 1+1 dimensions.

Numerical evidence suggests arbitrarily large negative energy densities are possible.

Results imply potential for large negative energy in wormhole constructions.

Abstract

Motivated by traversable wormhole constructions that require large amounts of negative energy, we explore constraints on the amount of negative energy that can be carried by a free Dirac field in a slab-shaped region between two parallel spatial planes. Specifically, we ask what is the minimum possible uniform energy density that can exist at some time, considering all possible states and all possibilities for the physics outside the slab. The vacuum state where we identify the two sides of the slab with antiperiodic boundary conditions gives one possible state with uniform negative energy, but we argue that states with more negative energy exist above 1+1 dimensions. Technically, we reduce the problem to studying a massive Dirac field on an interval in 1+1 dimensions and numerically search for states with uniform energy density in a lattice regulated model. We succeed in finding states with enhanced negative energy (relative to the antiperiodic vacuum) which also appear to have a sensible continuum limit. Our results for the mass-dependence of the minimum uniform energy density in 1+1 dimensions suggest that for a 3+1 dimensional massless Dirac fermion, it is possible to have states with arbitrarily large uniform negative energy density in an arbitrarily wide slab.