Negative Energy Density States for the Dirac Field in Flat Spacetime

TL;DR

This paper investigates negative energy densities in the Dirac field, demonstrating unbounded energy from below in certain superpositions and confirming quantum inequalities, while contrasting with scalar fields where such negativity cannot be produced.

Contribution

It provides a detailed analysis of negative energy densities in the Dirac field and compares these findings with scalar fields, highlighting the conditions for negativity.

Findings

Energy density in Dirac field is unbounded from below in certain superpositions.

Quantum inequalities for scalar fields are satisfied in Dirac field cases.

Negative energy densities cannot be produced in scalar fields using superpositions.

Abstract

Negative energy densities in the Dirac field produced by state vectors that are the superposition of two single particle electron states are examined. I show that for such states the energy density of the field is not bounded from below and that the quantum inequalities derived for scalar fields are satisfied. I also show that it is not possible to produce negative energy densities in a scalar field using state vectors that are arbitrary superpositions of single particle states.