I generally get the difference between matter particles (leptons and quarks) and “force carrying” particles (bosons). But I still do not understand how the “exchange” of fundamental / elementary bosons (e.g., photons and gluons) bind or ‘glue’ matter particles together as well as repel matter particles — as in attraction of oppositely charged particles and repulsion of identically charged particles (and the photon flux density in electromagnetic fields around charged particles and magnets). The typical Feynman diagram merely shows the interaction of a single photon (real or virtual, eh) between two electrons [1]. I get lost in the equations, of course. And most interesting cases may not even be solvable. On my wish list is a visualization at field scale [2] which advances an explanation for mere mortals (and does not involve playing catch with balls).

[I think that I get the Periodic Table and how sharing electrons between atoms (valence shell electrons) makes molecules (and therefore all stable matter), but not the Standard Model table and how “sharing” of bosons makes for attractive and repulsive forces.]

I’m fascinated by condensed matter physics without grasping the mathematics of Bose–Einstein statistics. Most of us grew up hearing about superfluids.

Lasers are possible because photons are bosons — indistinguishable particles in the same (quantum) state — and can pile up on each other. Frictionlessly sociable [“no significant interaction between the particles”]. But what’s the photon density in a laser pointer, eh?

Atoms exist — and the universe and mankind — because electrons are leptons and not bosons. In normal situations electrons cannot be packed together in the same state — they like some personal or private space.

And composite bosons are even trickier. It’s all about quantum spin.

So, this ThoughtCo article caught my attention: “What Is a Boson?” by Andrew Zimmerman Jones (May 27, 2019).

Fundamental bosons:

Photon– Known as the particle of light, photons carry all electromagnetic energy and act as the gauge boson that mediates the force of electromagnetic interactions.

Gluon– Gluons mediate the interactions of the strong nuclear force, which binds together quarks to form protons and neutrons and also holds the protons and neutrons together within an atom’s nucleus.

W Boson– One of the two gauge bosons involved in mediating the weak nuclear force.

Z Boson– One of the two gauge bosons involved in mediating the weak nuclear force.

… there are other fundamental bosons predicted, but without clear experimental confirmation (yet) … [Higgs, graviton, bosonic superpartners]

Composite bosons:

Mesons– Mesons are formed when two quarks bond together. Since quarks are fermions and have half-integer spins, if two of them are bonded together, then the spin of the resulting particle (which is the sum of the individual spins) would be an integer, making it a boson.

Helium-4 atom– A helium-4 atom contains 2 protons, 2 neutrons, and 2 electrons … and if you add up all of those spins, you’ll end up with an integer every time. Helium-4 is particularly noteworthy because it becomes a superfluid when cooled to ultra-low temperatures, making it a brilliant example of Bose-Einstein statistics in action.

##### Notes

[1] This several year old Physics Stack Exchange thread makes the point: “Feynman diagram for attractive forces.”

When you do this it doesn’t matter whether the lines look like they’re attracting or not, because you can deform the diagram any way you like (as long as you keep the same external lines).

The thing that tells you whether the force is attractive or repulsive is the math; if you use the electron-positron diagram to calculate the potential energy you will find that it corresponds to an attractive Coulomb potential; if you reverse the positron arrow so it now represents another electron (without moving the lines at all!), you will now find that the potential is repulsive.

The upshot here is that so-called “virtual particles”, which are internal lines in a Feynman diagram (in your examples those would be the photon, the gluon and the pion), are not actual particles being exchanged.They’re just a neat picture that helps visualizing the process, butin reality the particles are interacting through their quantum fields, and these fields are very hard (maybe even impossible) to understand intuitively.But remember that the diagrams in your post are what we call “tree level”. They’re the simplest diagrams for the given processes, but in reality there is an infinite number of them, with ever growing number of vertices and lines, and the more diagrams you calculate the more accurate your results will be.Feynman diagrams do not intent to show attraction nor repulsion. They are just a bookkeeping graphical tool [“eye candy”] for calculating such amplitude. You may use them though to find out if the interaction is attractive or repulsive.

[2] And visualizing somehow, despite limitations of any analogy or metaphor, the momentum transfer in field gradients.

I’m beginning to see more clearly how Feynman was a “particles guy,” as characterized by a few physicists. His purpose in quantum electrodynamics (QED) was calculation (“… just do the math”), and his diagrams were a novel and powerful way to organize the equations. And his sum over all possible paths (path integral formulation) may reflect that we are really talking about fields. Matter “particles” as quantum oscillations or localized vibrations within those omnidirectional fields. And interactions as perturbations of those pervasive continuous fields.

https://en.wikipedia.org/wiki/Feynman_diagram

Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula.As David Kaiser writes, “since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations”, and so “Feynman diagrams have revolutionized nearly every aspect of theoretical physics.”The calculation of probability amplitudes in theoretical particle physics requires the use of rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented graphically as Feynman diagrams.

…

a Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory.… Alternatively, the path integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state, in terms of either particles or fields.… Gerard ‘t Hooft and Martinus Veltman gave good arguments for taking the original, non-regularized Feynman diagrams as the most succinct representation of our present knowledge about

the physics of quantum scattering of fundamental particles.A Feynman diagram is a representation of quantum field theory processes in terms of particle interactions.When a group of incoming particles are to scatter off each other, the process can be thought of as one where the particles travel over all possible paths, including paths that go backward in time.[Like ripples in a fluid?]…

only the sum of all the Feynman diagrams represent any given particle interaction; particles do not choose a particular diagram each time they interact. The law of summation is in accord with the principle of superposition—every diagram contributes to the total amplitude for the process.A Feynman diagram represents a perturbative contribution to the amplitude of a quantum transition from some initial quantum state to some final quantum state.

https://en.wikipedia.org/wiki/Path_integral_formulation

The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral,

over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.However,

the path integral formulation is also extremely important in direct application to quantum field theory, in which the “paths” or histories being considered are not the motions of a single particle, butthe possible time evolutions of a field over all space. The action is referred to technically as a functional of the field: S[ϕ], wherethe field ϕ(xμ) is itself a function of space and time, and the square brackets are a reminder that the action depends on all the field’s values everywhere, not just some particular value. One such given function ϕ(xμ) of spacetime is called a field configuration. In principle, one integrates Feynman’s amplitude over the class of all possible field configurations.