To understand contemporary physics, particularly quantum theory, the Standard Model is essential. This article includes an excellent video overview:
• Quanta Magazine > Math Meets QFT > “A Video Tour of the Standard Model” by Kevin Hartnett, Senior Writer/Editor (July 16, 2021)
(quote) Physicists would like to move beyond the Standard Model to an even more encompassing physical theory.
And that, maybe, is where math comes in. Mathematicians will have to develop a fresh perspective on quantum field theory if they want to understand it in a self-consistent and rigorous way. There’s reason to hope that this new vantage will resolve many of the biggest open questions in physics.
The video is hosted and presented by Cambridge University theoretical physicist David Tong, and also available on YouTube:
• YouTube > Quanta Magazine > “The Standard Model: The Most Successful Scientific Theory Ever” (Jul 16, 2021)
(Description) The Standard Model of particle physics is the most successful scientific theory of all time. It describes how everything in the universe is made of 12 different types of matter particles, interacting with three forces, all bound together by a rather special particle called the Higgs boson. It’s the pinnacle of 400 years of science and gives the correct answer to hundreds of thousands of experiments. In this explainer, Cambridge University physicist David Tong recreates the model, piece by piece, to provide some intuition for how the fundamental building blocks of our universe fit together. At the end of the video, he also points out what’s missing from the model and what work is left to do in order to complete the Theory of Everything.
**Correction: At 13’50”, the photon should be included with the three fundamental forces. The animation here is incorrect, while the narration is correct.
Using helpful visuals, David Tong unpacks the Standard Model piece by piece – assembles the model from “the fundamental building blocks of our universe.” I like the way he points out two caveats early on:
- First, gravity is NOT included in the model, for two reasons:
(quote) The first is that, at the microscopic level, the force of gravity is so weak that it barely has any effect on a single subatomic particle. [But what about a “particle” on space-time?]
The second is that we don’t really know how to incorporate general relativity, which is a classical theory, into the quantum world.
- Second, quantum theory really is about fields – the language of “particles” is a convenient simplification.[1, 2]
(transcript) … the Standard Model is written in a language known as quantum field theory. This tells us that matter, at the fundamental level, is not really made up of particles. Instead, it’s made up of fields: fluid-like objects which are spread throughout all of space. These fields are engaged in an intricate, harmonious dance to a music that we call the laws of physics. The interactions between the fields produce the physical world in the form of particles. To understand the Standard Model, it’s more convenient to use the language of particles.
 Cf. my post “Reality is fields.”
As Sean Carroll noted in one of his lectures, “… you need to stop thinking of the world as particles. … That’s the secret we physicists have never told you.” (Particles as contextual realities.)
In my May 22, 2017 comment for “Reality is fields,” Paul Sutter noted:
(quote) In other words, you can slap a field and make some particles. A single particle is just the minimum possible amount of energy that a field can support. Every kind of particle that scientists know of, from the electron to a photon, is associated with its own space-time-filling vibrating field.
 See also this older YouTube video of David Tong’s lecture “Quantum Fields: The Real Building Blocks of the Universe.”