It makes a lot more sense if you have the historical context though. When this is taught the context is left out and then it feels more like mathemagics to me and probably others as well. Maybe there are good books that explain this from a historical point of view, while still teaching the theory, but they must be pretty rare.
My comment (the GG..GGP) was an (over)reaction to the posted article. The article presents the new approach like a very "natural" explanation, but there are already some other "natural" explanations.
In a Physics degree, the order is quite historical. Like one full course for the three first next items, and all the other together. I'm not sure if there is a book with all of them, you probably need 4 or 5 books.
1) Non-Quantum Non-Relativistic Electromagnetism
2) Quantum Non-Relativistic Electromagnetism
3) Non-Quantum Relativistic Electromagnetism
4) Quantum Relativistic Electromagnetism
5) By the way, you can interpret the Quantum Relativistic Electromagnetism as a U(1) symmetry. (my comment)
6) It looks like a good idea. Let's use other groups to explain other known forces: the weak and strong force. (The G...GP comment about SU(2) and SU(3).)
7) ???
[See note 1]
For some reason, popular science articles love to show something almost magical and prefer to present something like the "5)". It makes it easier to hide the math and use hand waving.
Also, Physicist working in physic particle also believe that "5)" and "6)" are the correct approach, and the other are just useful for teaching and for historical reasons. But to discover "7)" it's better to think about some weird new symmetry group [2].
For examples, a few years ago, it was popular to think the next step "7)" was using a new group SU(5) that combines SU(2) and SU(3). The problems is that the experiments gave different results than then new proposed theory, not too bad but like 1% off. I still remember my professor talking about how great was SU(5) and how the experiment disagree, and he looked heartbroken because he really liked SU(5).
[1] You should add some material about the historical discovery of the weak and strong forces between "5)" and "6)".
[2] Other's prefer superstrings for "7)", there are other approach, but all are weird.
