Feynman diagrams are (much!) more than pretty pictures of particles colliding: they represent math. A high level overview of how to turn a diagram into its underlying mathematical expression is

Kaiser, David, "Physics and Feynman's diagrams," American Scientist 93:156-165 (2005).

The original paper of course goes into much more detail:

Feynman, Richard P., "Space-time approach to quantum electrodynamics," Physical Review 76:769-789 (1949).

One key idea is that a given Feynman diagram is always just a representative of a horde; it is merely one (perhaps the simplest) of an infinite number of other Feynman diagrams expressing all the ways (often higher order ways) the given particles could interact. All these ways need to be summed to compute some quantitative property about the given QED particle interaction.

While Feynman diagrams simplify the task of turning a given diagram into a mathematical expression, enumerating all the possible Feynman diagrams for a given interaction remains nontrivial.

## No comments :

Post a Comment