Dyson equation

The Dyson equations are correlations found by Freeman Dyson between different S-matrix elements and Green's functions, a quantum field theory. Although the equations of Dyson were infinitely found only for two -and three- point functions in quantum electrodynamics by adding up many Feynman diagrams, but these equations are general in quantum field theories and are also used for general n-point functions.

Make the full ( dressed ) renormalized Green's functions is by a non-interacting component, the so-called naked (bare ) Green's functions, and an interaction- prone part, which includes all possible interactions of the fields involved. Mathematically, it is integral equations.

Are the original Dyson equations

For the electron propagator:
For the photon propagator:
And the electron-photon vertex:

Where the subscript 0 denotes respectively the free terms and the large Greek letters each representing irreducible Green's function for the one-particle system, ie, the electron self-energy and the photon vacuum polarization.

The first two equations are Einteilchenfälle (n = 1 ) of the general form

With the Green function for n free particles, the full Green's function of the n - particle irreducible and the interactions of the n particles. This equation is now often referred to as the Dyson 's equation.

The Dyson equation, in the form of the Dyson -Schwinger equations is used today in many areas of theoretical physics.

Dyson equation

See also