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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.

herisson
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Seub
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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
  • Just an opinion, but including the dash seems like the safest bet. – ScotM Mar 12 '15 at 22:10
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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
  • So, hyphens all the way? You know, a lot of these words are not real words, in the sense that in mathematics you often call "non-" an object that is not . Non-commutative, non-singular, etc. There are also a lot of concepts that are named "quasi-", "hyper-", "pseudo-", "almost-" etc etc. I was wondering if there is a general rule to follows when to write these words. – Seub Mar 12 '15 at 22:57
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    http://english.stackexchange.com/questions/889/when-is-it-necessary-to-use-a-hyphen-in-writing-a-compound-word – Good A.M. Mar 12 '15 at 23:07
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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 00:11
  • Sounds like a reasonable approach, however it appears to me that mathematicians (including the most prominent ones) (1) don't have a consensus when it comes to writing these words and (2) could care less, for most of them. – Seub Mar 13 '15 at 00:19
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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 00:36
  • It seems to me that for consistency, it would be a good habit to always hyphenate 'non', 'quasi', 'hyper', etc. on the grounds that depending on what follows, it can be hard to analyse an unfamiliar compound with the eye. 'Nonabelian' is a good example: when I first saw that today, I had to look twice before going back 40 years and thinking, 'Ah, abelian = commutuative'. – David Garner Mar 15 '15 at 20:26
  • FWIW, the OED has non-abelian, hyphenated and not capitalized; however, two of their three attestations are capitalized (and hyphenated). Non-degenerate is also hyphenated in the OED, not as its own entry but only under the entry for the prefix non-. Kähler doesn't appear at all, with or without non-, but I think it would be fair to guess that the OED would prefer hyphenation (whether it would drop the capitalization I can't guess). – 1006a May 27 '17 at 20:18
  • Sounds like you either find someone whose style you want to imitate, or you develop your own typographical conventions (generally after tenure). In any event, if it matters, your editor will change it for you. Me, I always write it non-Abelian, on those rare occasions I do so. – John Lawler Nov 16 '19 at 00:26

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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).

Mitch
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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."

Lopey Tall
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