Comparing two methods of regularization of the kinetic energy density

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.