In general
It's . . . a judgement call - and that's coming from someone who probably makes some poor judgement calls in this area from time to time.
If you're going to write an answer that you think is pretty in-depth and goes above and beyond the call of duty, ask yourself this:
- Is it necessary to go the extra mile? Will I be raising readers to a new plane of enlightenment and understanding? Will I just be showing off? There's a difference, and sometimes you risk people not reading the answer because there's a lot of unnecessary fluff.
- Will the OP and other readers understand what I'm writing? I'm sometimes guilty of not asking myself this, which probably means that some folks just gloss over some of my answers. And that's fine. But you need to make sure that the people who would ask this question - the OP and future would-be askers - actually understand your answer. Otherwise, it might as well be written in Linear A.
- Did I explain everything properly? It's okay to add some jargon if jargon has a place there, but you need to explain things, at least the first time around.
This case
I consider myself somewhat educated in physics, though not to a great extent in this particular area. In other words, I know the math behond some Lagrangians, Noether's theorem, and how you can find solutions to various forms of the Schrödinger equation, all of which play a role in the answer. But then I get to this section:
$\mathcal{L}_{Yukawa}$ is, of itself, still quite long, containing terms such as $$\sum_{f' = l_R, f = l_L}H_{f'f}\bar{f'}\left(f \circ \phi \right) $$
Here, $H$ is a 3×3 matrix, $\bar{f'}$ are anti-right-handed leptons (aka. positrons), $f$ are left-handed leptons (electrons and neutrinos) and $\phi$ is ... The Higg's field. Or, the only way that elementary particles can have mass is from the Higgs boson. This includes, to my knowledge, neutrinos.
. . . It gets a bit blurry there. I know all the words, but we've got more than words here. We've got math. And I have only a very faint idea of what that summation means.
I think this part violates Bullet 1 (I don't really need to know what the Yukawa term is mathematically, unless the point is to emphasize how complicated it is, in which case, mission accomplished!), Bullet 2 (for most people, I'd reckon), and Bullet 3 (yes, the symbols were explained, but not as mathematical objects, which makes the expression itself useless).
That said, I think that the above is the one place in the answer where the writer maybe went overboard. Breaking down the Standard Model Lagrangian is a nice touch to make sure we all know the background, and the end reminds me that I'm always a sucker for time evolution and quantum states (plus, that section makes a good mathematical point).
So, yes, there are cases where it's probably best to limit oneself in an answer for the pure sake of readability. You do have to know who your audience is at the present and likely will be in the future. You also have to make it clear what your mathematics means, because inconsistency in notation is no small problem. Finally, let's make sure that we only write what we need to write in an answer - and yes, I could take that advice once in a while.