Comparing two methods of regularization of the kinetic energy density

TL;DR

This paper compares two regularization methods for the kinetic energy density of a massless scalar field in a static potential, revealing they produce different results with one method including an ambiguous term.

Contribution

It introduces a comparison between subtraction and point split regularization methods, highlighting their differences and the presence of an ambiguous term in one approach.

Findings

The two regularization methods yield different results.

Point split regularization introduces an ambiguous term.

Subtraction method removes the cosmological constant from the naive expression.

Abstract

In this paper we will compare two different methods of regularizing the kinetic energy density for a massless scalar field in the presence of a static scalar potential. One method of regularization is to subtract the cosmological constant from the "naive" expression for the kinetic energy density. The other method is to use point split regularization. It is found that the two methods yield different results. The result obtained using point split regularization includes an extra ambiguous term.