The effect of point split regularization on the sign of the Casimir energy

TL;DR

This paper investigates how point split regularization affects the sign of Casimir energy for a Dirac field, revealing that the regularization method can lead to negative Casimir energies contrary to previous positive results.

Contribution

It demonstrates that the choice of charge density operator definition via point splitting can alter the sign of the Casimir energy, challenging prior assumptions.

Findings

Point splitting introduces an extra term in charge density.

Casimir energy can be negative with point split regularization.

Previous positive results are affected by regularization choices.

Abstract

In a recent paper [1] the Casimir energy was calculated for a massive dirac field in (1+1) dimensional space-time in the presence of an inverse square well potential and shown to be positive. It will be shown that this result violates a key assumption of quantum field theory which is that the vacuum state is the state of minimum energy. The reason for this discrepancy is examined and is shown to be related to the way the charge density operator is defined. If the charge density operator is defined using point splitting then an extra term will be added to the charge which will result in the Casimir energy being negative.