Is it possible to create an negative energy space or area using electromagnetism in varied methods?

Question

My question "Is it possible to create an negative energy space or area using electromagnetism in varied methods" is very general. I understand that, but at this time and instance I ask that you all humor me as I can not narrow it down further.
My question originates from the possibility of creating an compression field using electromagnetism in an unascertained method. The general hypothesis will have varied application, one being the measurement of negative energy and as of which the further applications will domino effect further out. 

Comments

There are two very well known examples of the "negative energy in space", namely, in interactions of charged particles. For example, a proton "creates" a negative potential energy for an electron, so they attract each other and tend to get closer. The closest state, though, is not something of a zero size, but a Hydrogen atom.

The same proton "creates" a positive potential energy for another proton or another positively charged particle, so they repulse each other.

Concerning QFT, there is a phenomenon called annihilation and it happens that an electron and a positron may create a Hydrogen-like "positronium" atom, but it is unstable and decays into several photons.

If you are speaking of the electromagnetic field energy solely, it is a positively defined quantity since it is an integral of positive functions $\int\left(E^2+H^2\right)dV$. But you should keep in mind that the fields have their "sources" and "sinks" - charged particles in motion.