Potential Energy of a Quantum Field

The energy associated with a field can arise in different ways.

Usually energy of a field comes about because the field is changing from point to point in spacetime (there is energy in the stretching associated with the changing field values, much like there is energy in the twists or vibrations of a sheet of rubber).

But in addition to that, fields can carry energy just by sitting there with some fixed value. That kind of energy, associated with the value of the field itself (rather than the changes in the field from place to place or time to time), is known as "potential energy".


Vibrations in quantum fields give rise to particles. If a field is constant everywhere, so there are no vibrations, you don't see any particles.

The background value of a field - the average value it takes when we imagine smoothing out all the vibrations - is not directly observable. Nevertheless, it can be indirectly observable, as this "potential energy" can affect the curvature of spacetime.

Potential energy can be converted into other sorts of energy.