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I asked this question on Mathematics Stack Exchange (here) but I haven't had any luck so far. Allow me to copy the question:

If I wanted to be scrupulous about correct spelling, is there any reason that I should prefer either:

  • non-abelian or nonabelian?
  • nondegenerate or non-degenerate?
  • hyperkähler or hyper-Kähler?

NB: For some reason, hyperkähler is more common than hyper-Kähler, however quasi-Fuchsian is more common than quasifuchsian, and I don't think anyone writes "pseudoriemannian".

While I'm at it, allow me to ask a second spelling question: should I write PDEs or PDE's? It seems to me that there is no reason to use an apostrophe but a lot of people do.

PS: Wikipedia says something about the use of lowercase "a" in "abelian": here.

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    Either Wikipedia is confused, or they are all acceptable :-) Non-abelian? ... Non-degenerate? ... hyper-Kähler? manifold ... Search hyper-Kähler manifold but > hyperKähler? manifold – ScotM Mar 12 '15 at 22:05
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    @ScotM Including a dash is totally wrong. Including a hyphen is often a valid choice. These words are non-central enough not to be included in most dictionaries. OED will probably include them, and their spellings may be assumed correct. – Edwin Ashworth Mar 12 '15 at 22:26
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    If you feel memorial about Nils Abel, by all means capitalize abelian. Frankly, I think making it into lowercase is a mark of true immortality, especially with a property as basic as commutativity. As for hyphens, follow the traditions established by the current writers you most admire. If they write well, write the same way. Imitation is the sincerest form of learning. – John Lawler Mar 13 '15 at 0:11
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    Well, that's why I tried my luck in the English language stackexchange after the maths one. I admit it's not a fascinating question, but when you're a mathematician author you write these words hundreds of times, and after a while the uncertainty/inconsistency gets annoying. But maybe it's just me. For instance I just checked out a paper of Fields medalist McMullen (who I think writes very well), you have "non-constant" and "nonconstant" in the same paper. – Seub Mar 13 '15 at 0:36
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Three specific answers:

That is what is, but you're probably asking for what should be. In general though, the orthographic trend is at first for 'non' followed by a name-adjective, just like any noun-noun pair, is to go through successive states of neologism: - 'non' followed by a hypen then followed by the capitalized name, eg 'non-Abelian' - 'non' followed by a hyphen then followed by the uncapitalized name, eg 'non-abelian'. - 'non' followed directly by the uncapitalized name, eg 'nonabelian'.

This is because the name part of the word is, at first, very distinctive and meaningful as a name, but slowly becomes opaque, and eventually a regular word, similar genericization, how a trademarked company name, like Kleenex or Google, becomes a corresponding generic, kleenex (for any kind of facial tissue) or google (to search the internet using any search engine).

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Physics nomenclature:

Zee's QFT in a Nutshell, and Srednicki's QFT use "nonabelian."

Lancaster & Blundell's QFT for the Gifted Amateur, Tong's Lectures Noted on QFT, Schwartz's QFT and the Standard Model, and Peskin & Schroeder's Intro to QFT use "non-Abelian."

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