# Fundamental Interactions in the Standard Model

The elementary particles of the Standard Model seem clearly enumerated and distinguished, totaling 17 (6 quarks, 6 leptons, 4 gauge bosons, and the Higgs). Is there a similar enumeration of the variety of fundamental interactions found in nature according to the Standard Model? If it is finite, how many particular interactions are there (ie, in terms of the 17 elementary particles), and is every such interaction expressible as a Feynman Diagram? Thanks.

EDIT: To clarify, I was asking about how many total interactions like ($$e^- + e^+ \rightarrow \mu^- + \mu^+$$) and ($$e^- \rightarrow e^- + \gamma$$) there are.

EDIT2: The Wikipedia article on "Fundamental interaction" says: "The interaction of any pair of fermions in perturbation theory can then be modelled thus: Two fermions go in --> interaction by boson exchange --> Two changed fermions go out." This seems to imply that the total number of possible interactions is $$N(N-1)/2$$ (if interactions of like particles are excluded). Since there are 12 fermions, the number of interactions amounts to 66. Are all such interactions found in nature?

• The 19 parameters listed at en.wikipedia.org/wiki/Standard_Model#Theoretical_aspects should suffice depending on how you count. Dec 11, 2021 at 22:29
• One can look up the Feynman rules of the standard model, the list is finite with the field content of the SM (even rules involving gravitons can be found). Though the number of Feynman diagrams is infinite. Dec 11, 2021 at 22:55
• Dec 12, 2021 at 7:34
• In a reaction equation, you can have as many particles as you want on the left hand side. So in the sense of edit 1, the number of interactions is infinite. If you're just interested in pairs of fermions (and you consider two quarks to be the same fermion regardless of color) then the answer is something like 66. Dec 13, 2021 at 10:14

There are two standard models, one of particle physics that focuses on elementary particles and the three fundamental so-called gauge forces: the weak, strong and electromagnetic force; the other is of cosmology, which focuses on very large scale phenomena mediated by gravity which is both taken to be a fundamental force and not a force at because, after General Relativity, it is seen as an expression of the curvature of spacetime. But this is chimerical, as the gauge forces can also be writren geometrically.

In particle physics, the four gauge bosons are the W, Z, photon and gluon. They mediate the three gauge forces. They are called gauge forces because they forces exhibit a symmetry called gauge symmetry. In fact, just as gravity can be formulated geometrically, so can these three forces through the notion of fibre bundles. Here, the physical notion of a gauge symmetry is encapsulated through a connection on the bundle. This in turn tells us how the bundle curves. Thus, we see the three gauge forces has a geometrical expression akin to that of General Relativity.

Now, the quanta of these forces are the gauge bosons: W, Z for the weak force; the gluon for the strong force and the photon for the electromagnetic force. All of these particles have been detected.

In the cosmological standard model, the only force is gravity. This has not yet been quantised successfully. Its hypothetical quanta is called the graviton. This too is a boson. It hasn't yet been detected.

• Based on your description, is it reasonable to a first approximation for a neophyte to "visualize" each of the gauge bosons (plus the graviton) as localized quantum disturbances in 4 separate spatiotemporal overlapping fields: an electromagnetic field, a strong field, a weak field, and a gravitational field? Dec 12, 2021 at 19:08
• The gauge bosons are called "particles", but is there a more perspicuous term available? (I used "disturbance in a field" above as a synonym, but not sure if this could be seriously misleading.) More to the point, can all elementary particles (fermions + bosons) be considered as "disturbances"? Dec 12, 2021 at 19:09
• That's how I think about them. There can be a large zoo of disturbances (extended objects) but particles are a commonly occurring type. Dec 14, 2021 at 15:30

The text Particles and Fundamental Interactions (2009) by Braibant, Giacomelli, and Spurio states that there are a total of 61 elementary particles in the Standard Model (p 314). The total consists of 24 fermions + 24 antifermions + 12 vector bosons + 1 Higgs boson.

Considering only fermion-fermion interactions then gives a total number of potential interactions of N(N+1)/2, where N=48. The maximum potential number of fermion-fermion interactions is thus 1176.

However, note that "the full theory includes perturbations beyond simply fermions exchanging bosons; these additional perturbations can involve bosons that exchange fermions, as well as the creation or destruction of particles ..." (ref: Wikipedia-Fundamental interaction).