Feynman diagram

A Feynman diagram records a term in the perturbative expansion: edges represent propagators, vertices represent interactions, and loops represent unconstrained momentum integrals.

Feynman rules translate each diagram into momentum-space factors for propagators, vertices, external states, momentum conservation and loop integration.

Feynman parameter

\frac{1}{A B} = \int_{0}^{1} \frac{d x}{[ x A + ( 1 - x ) B ] ^{2}} .

After a momentum shift, this often converts a loop integral into a rotationally symmetric one.

A tree-level diagram has no loops and gives the leading classical contribution allowed by the interaction vertices.

L = I - V + 1

of independent momentum cycles, where

I

is the number of internal lines and

V

the number of vertices. Each loop introduces an unconstrained momentum integral.

A connected Feynman diagram has a path between every pair of its vertices. Normalized correlation functions discard disconnected vacuum bubbles, while full correlators can still factor into disconnected components carrying external insertions.

A one-particle-irreducible Feynman diagram is a connected Feynman diagram that remains connected after any one internal line is cut. The vertices of the quantum effective action generate precisely these diagrams.

There are no discussions about this article yet.

A Feynman diagram is a graphic representation used in quantum field theory to visualize and analyze the behavior of subatomic particles during interactions. Named after physicist Richard Feynman, these diagrams depict the interactions between particles, such as electrons, photons, and gluons, in a way that makes complex calculations more manageable. In a typical Feynman diagram: - **Lines** represent the particles.

I think they are a tool to calculate the probability of different types of particle decays and particle collision outcomes. TODO Minimal example of that.

And they can be derived from a more complete quantum electrodynamics formulation via perturbation theory.