Some ambiguities with point split regularization and its impact on a proof of the spatial quantum inequality

TL;DR

This paper investigates ambiguities in point split regularization affecting the proof of the spatial quantum inequality in quantum field theory, highlighting potential issues with existing proofs due to regularization ambiguities.

Contribution

It identifies and analyzes ambiguities in point split regularization that may compromise the validity of the proof of the spatial quantum inequality.

Findings

Potential problems with the existing proof due to regularization ambiguity

Highlights the need for careful regularization in quantum inequality proofs

Questions the universality of the quantum inequalities in certain cases

Abstract

In classical physics the energy density of a field is always positive. However this does not hold true for quantum physics where the energy density of a field can be locally negative. There are limits on the weighted average of this negative energy density called the quantum inequalities. Recently this author has provided a number of examples which show that the quantum inequalities are not valid. In this paper we will examine a previously published proof of the spatial quantum inequality for a zero mass scalar field in 1-1 dimensional space-time. It will be shown that there is a possible problem with this proof due to an ambiguity associated with point split regularization and the definition of the Hadamard form for the two point function.