Feynman Diagram

Feynman diagram, a graphical method of representing the interactions of elementary particles, invented in the 1940s and ’50s by the American theoretical physicist Richard P. Feynman. Introduced during the development of the theory of quantum electrodynamics as an aid for visualizing and calculating the effects of electromagnetic interactions among electrons and photons, Feynman diagrams are now used to depict all types of particle interactions.

A Feynman diagram is a two-dimensional representation in which one axis, usually the horizontal axis, is chosen to represent space, while the second (vertical) axis represents time. Straight lines are used to depict fermions—fundamental particles with half-integer values of intrinsic angular momentum (spin), such as electrons (e⁻)—and wavy lines are used for bosons—particles with integer values of spin, such as photons (γ). On a conceptual level fermions may be regarded as “matter” particles, which experience the effect of a force arising from the exchange of bosons, so-called “force-carrier,” or field, particles.

At the quantum level the interactions of fermions occur through the emission and absorption of the field particles associated with the fundamental interactions of matter, in particular the electromagnetic force, the strong force, and the weak force. The basic interaction therefore appears on a Feynman diagram as a “vertex”—i.e., a junction of three lines. In this way the path of an electron, for example, appears as two straight lines connected to a third, wavy, line where the electron emits or absorbs a photon. (See the figure.)

Feynman diagrams are used by physicists to make very precise calculations of the probability of any given process, such as electron-electron scattering, for example, in quantum electrodynamics. The calculations must include terms equivalent to all the lines (representing propagating particles) and all the vertices (representing interactions) shown in the diagram. In addition, since a given process can be represented by many possible Feynman diagrams, the contributions of every possible diagram must be entered into the calculation of the total probability that a particular process will occur. Comparison of the results of these calculations with experimental measurements have revealed an extraordinary level of accuracy, with agreement to nine significant digits in some cases.

Feynman diagram

The simplest Feynman diagrams involve only two vertices, representing the emission and absorption of a field particle. (See the figure.) In this diagram an electron (e⁻) emits a photon at V₁, and this photon is then absorbed slightly later by another electron at V₂. The emission of the photon causes the first electron to recoil in space, while the absorption of the photon’s energy and momentum causes a comparable deflection in the second electron’s path. The result of this interaction is that the particles move away from each other in space.

Feynman diagram

One intriguing feature of Feynman diagrams is that antiparticles are represented as ordinary matter particles moving backward in time—that is, with the arrow head reversed on the lines that depict them. For example, in another typical interaction (shown in the figure), an electron collides with its antiparticle, a positron (e⁺), and both are annihilated. A photon is created by the collision, and it subsequently forms two new particles in space: a muon (μ⁻) and its antiparticle, an antimuon (μ⁺). In the diagram of this interaction, both antiparticles (e⁺ and μ⁺) are represented as their corresponding particles moving backward in time (toward the past).

Feynman diagram

More-complex Feynman diagrams, involving the emission and absorption of many particles, are also possible, as shown in the figure. In this diagram two electrons exchange two separate photons, producing four different interactions at V₁, V₂, V₃, and V₄, respectively.