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

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.