An example of a violation of the spatial quantum inequality with a comment on the quantum interest conjecture

It is generally known that the energy density can be negative in quantum field theory. It is also believed that there are limits on this negative energy density. These limits are known as the quantum inequalities. In a recent paper [8] an example was provided of a system which violated the quantum inequalities. Here we will demonstrate a violation of the spatial quantum inequality for a scalar field with zero mass in 1-1 dimensional space-time. In addition we will show that the system presented here also violates the quantum interest conjecture.