The Feynman diagram, named for Richard Feynman who introduced them in 1948, provides a graphical representation of the nature of particle interactions in the Standard Model. The implication of each such diagram is to add terms into a cumulative Lagrangian describing the full interaction picture. Furthermore, the Standard Model assumes that fundamental particles are point-like particles, which then affects the nature of the interaction terms that are computed, which is ultimately what drives the need for renormalization, due to the increasingly high force-field strengths at increasingly short distances from these point particles (e.g., Wallace, 2011; Fraser & Rejzner, 2024).
Figure 1:
Elementary force interactions in the Standard Model. All Feynman diagrams in the model can be constructed from combinations of these vertices. q is any quark, g is a gluon, X is any charged particle, γ is a photon, f is any fermion, m is any particle with mass (with the possible exception of the neutrinos), \(m_B\) is any boson with mass. In diagrams with multiple particle labels separated by /, one particle label is chosen. In diagrams with particle labels separated by | the labels must be chosen in the same order. For example, in the four boson electroweak case the valid diagrams are WWWW, WWZZ, WWγγ, WWZγ. Adapted from Ponor/Wikimedia.
Figure 1 shows the elementary force interactions in the Standard Model, using Feynman diagrams. Although these diagrams look like actual spatial trajectories of particles moving through 3D space, that is very much not the case. Instead, each such diagram corresponds to factors that must be added to an underlying path integral formulation, which is then computed in the field theory framework of Fourier (Fock) space, which only represents energy / momenta, and has no spatial information at all.
Critically, the path-integral framework computes all possible ways in which some kind of particle interaction could possibly take place, including different spatial locations and other such parameters, with the predicted results being probabilities of observing the corresponding specific outcomes across many different repeated trials of a specific kind of particle interaction. In this way, the overall framework retains the core Copenhagen probabilistic / epistemic approach, and the infinities and other complexities resulting from the path integral framework (see renormalization) have generally obscured the interpretation of Feynman diagrams as reflecting discrete, nonlinear particle interactions.
By dealing only in momentum / energy space, the field theory framework massively simplifies the problem relative to having to explicitly deal with computing probabilities over different spatial trajectories. It is this joint calculation across these complementary basis representations, with the localization remaining implicit in the interactions that are computed, that enables the framework to capture the relevant phenomena.
Nevertheless, the underlying Standard Model theory holds that all fundamental (non-composite) fermion particles such as an electron or a quark are point particles, and that their interaction is mediated by the EM field as described by Maxwell’s equations, which falls off as a function of \(1/r^2\) in force magnitude. Thus, these spatial localization properties are built into the nature of the particle interactions.