Space-Time Approach to Quantum Electrodynamics
Draw the picture; read the amplitude straight off it. Lines, vertices, diagrams.
What if the maddening arithmetic of how light and matter interact could be replaced by a doodle — a few lines and dots you can sketch on a napkin?
The idea, unpacked
By the late 1940s, physicists could write down the laws governing electrons and light, but actually computing anything from them meant pages of grinding algebra, riddled with infinities that made answers come out as nonsense. The theory worked in principle and choked in practice.
Feynman's move was to draw a picture. Each particle becomes a line, each moment two particles interact becomes a dot where lines meet, and the whole tangled calculation becomes a small diagram. Then a fixed set of rules turns the picture back into a number — the probability of the process. Instead of bookkeeping, you draw what happens and read off the answer.
Where it came from
After the war, experiments grew precise enough to see tiny shifts in atoms that the old theory couldn't explain. Three physicists raced to fix it: Julian Schwinger and Sin-Itiro Tomonaga built rigorous, heavily mathematical machinery; Feynman, at Cornell, built his pictures. The approaches looked so different that few believed they were the same theory — until Freeman Dyson proved that all three gave identical answers. The 1965 Nobel Prize went to Feynman, Schwinger, and Tomonaga together.
Why it mattered
Feynman's diagrams didn't just match the others — they were far easier to use. A calculation that took an expert weeks could be set up by drawing the relevant diagrams and translating each into an integral. That ease is why the diagrams spread through physics like wildfire and became the everyday language of the field. They also carried a startling idea, borrowed from Stückelberg: a particle of antimatter — a positron — can be treated as an ordinary electron travelling backward in time.
A way to picture it
Think of a wiring diagram for a circuit. You don't trace every electron; you draw the components and the connections, and a few rules tell you the current. Feynman diagrams are the wiring diagrams of particle physics: lines are particles, dots are interactions, and the rules convert the sketch into the strength of the process. Play with one below — slide the energy of the exchanged photon and watch how strongly the two electrons push on each other.
Where it sits
This is the practical engine of quantum electrodynamics, the most accurately tested theory humans have — and it grew straight out of the quantum revolution of Planck, Einstein, and Dirac. The same picture-and-rules method later carried over to the forces inside the atomic nucleus, and the diagrams remain the first thing a physicist sketches when a new particle is found. When you read about collisions at the Large Hadron Collider, the predictions being tested were set up as Feynman diagrams.
In this paper two things are done. (1) It is shown that a considerable simplification can be attained in writing down matrix elements for complex processes in electrodynamics. Further, a physical point of view is available which permits them to be written down directly for any specific problem.
A complete, unambiguous, and presumably consistent, method is therefore available for the calculation of all processes involving electrons and photons.
The simplification in writing the expressions results from an emphasis on the over-all space-time view resulting from a study of the solution of the equations of electrodynamics.
For example, in the exchange of a quantum between two electrons there were two terms depending on which electron emitted and which absorbed the quantum. Yet, in the virtual states considered, timing relations are not significant.
Unfortunately, the modification proposed is not completely satisfactory theoretically (it leads to some difficulties of conservation of energy). It does, however, seem consistent and satisfactory to define the matrix element for all real processes as the limit of that computed here as the cut-off width goes to zero.