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

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.

arXiv comment21 pages

References in corpus (5)

• Restrictions on Negative Energy Density in Flat Spacetime
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• Quantum inequalities in two dimensional Minkowski spacetime
• Bounds on negative energy densities in flat spacetime
• The Quantum Interest Conjecture