Self-energy

In quantum field theory, self-energy

Σ

{\displaystyle \Sigma }

is the energy of a particle due to the interaction with its own field. In electrostatics, an electron is never really free. It is always interacting with its own electric field, independent of the environment it is in. In condensed matter physics, self-energy creates quasiparticles and gives them a lifetime. Self-energy is especially used to describe electron-electron interactions in Fermi liquids. Another example of self-energy is found in the context of phonon softening due to electron-phonon coupling.

Characteristics

Mathematically, this energy is equal to the so-called on mass shell value of the proper self-energy operator (or proper mass operator) in the momentum-energy representation (more precisely, to

ℏ

{\displaystyle \hbar }

times this value). In this, or other representations (such as the space-time representation), the self-energy is pictorially (and economically) represented by means of Feynman diagrams, such as the one shown below. In this particular diagram, the three arrowed straight lines represent particles, or particle propagators, and the wavy line a particle-particle interaction; removing (or amputating) the left-most and the right-most straight lines in the diagram shown below (these so-called external lines correspond to prescribed values for, for instance, momentum and energy, or four-momentum), one retains a contribution to the self-energy operator (in, for instance, the momentum-energy representation). Using a small number of simple rules, each Feynman diagram can be readily expressed in its corresponding algebraic form.