Self-energy

In classical physics is meant by the self-energy, the potential energy of a charge distribution in their own field. Some authors additionally the field energy involve with.

Self-energy is called in quantum field theory, the perturbative corrections to the propagator.

Classical use

The classical concept of the self-energy separates the charge and the field generated by it, and then figure out which energy would be needed to bring the charge in this field.

The electric potential of a point charge located at the position is given locally by

If at this point the point charge itself in this field, the expression diverges when goes.

Application

We assume, however, that the point charge of a particle passes only to a distance to the origin of the potential, we obtain a finite expression

Substituting this energy to the rest energy are equal, one obtains for the classical electron radius.

Field energy of a homogeneously charged sphere

Electric field:

Inside

Field energy:

Quantum field theory

In quantum field theory called the self-energy (including mass term ) the contributions of all diagrams with an incoming and an outgoing line. As of irreducible self-energy insertion () a self-energy insertion is referred to, which can not be decomposed by separating a line into two separate portions. There are thus not detected, for example in this case, the diagrams that follow several loops separately one after the other. The self-energy is then defined as the sum of contributions of all irreducible self-energy Bays:

A self-energy diagram is called skeletal if it is composed exclusively of propagators that do not involve self-energy insertions, ie loops. An energized skeleton is a skeleton of the development of the self-energy, in which each free propagator has been replaced by a propagator, which was corrected for the self-energy. Thus, the self-energy is the sum of contributions from all dressed skeletons. The presentation of self-energy as the sum of contributions from all dressed skeletons and the Dyson equation form a system of equations to be solved simultaneously ( self-consistently ). This can be done iteratively, can be canceled until at self-consistency. This leads to the self-consistent renormalization.

The simplest case of the Dyson equation (two-point function) looks straight at the self-energy.