If Particle Physics is the name of the game, the Standard Model is its cast of playable characters (just don’t get too comfortable, we think the roster could be expanding!). As different characters in a video game have different attributes – skills and statistics which define how they stack up against the rest of the crew—the fundamental particles forming the Standard Model are defined in terms of their Quantum Numbers which appear in the box corresponding to each particle. Some of these quantum numbers are quite familiar: take charge for example (the second number from the top in each box), others are somewhat more esoteric: spin (the third number from the top), I’m looking at you!
What these Quantum Numbers all have in common is that they represent the fact that the “particles” of the Standard Model aren’t really “particles” at all, or at least they're not just particles. I know what you’re thinking, “but you said Particle Physics was the name of the game!”, well, it turns out that this game has more than one version, and Particle Physics Version 2.0 is called Quantum Field Theory, or, for those in the know, QFT.
To get straight to the meat of the idea, QFT associates with each type of particle in the Standard Model something called a Quantum Field. A field is just a mathematical object which assigns a number or set of numbers to every point in space and time. A more familiar example of a field might be the Temperature Field which tells us what the temperature is at any place and time. Ostensibly, the quantum field of any given particle, say an electron, tells us how many of that particle are located at a given location.
This underscores the very important idea that there is only one quantum field for every type of particle, not a quantum field for every individual particle. Every single electron there has ever been, is, or will be is represented by the electron field. To this end, we can also think of a particle field as a kind of foundry or factory where a given particle is constructed. Each particle field is endowed with the ability to create or destroy its designated particle type at any place or time.
The existence of a field to accompany every particle (type) is what allows the fundamental particles to interact with each other without ever needing to come into direct contact (think the US and Soviet Union exerting their “spheres of influence” on one another during the Cold War). This is where the Quantum Numbers come into play. Each quantum number tells us something about how a given particle interacts with all the other particles in the model.