so one of the things these alqc-like posts coupd be great for is educational material
 https://en.wikipedia.org/wiki/Abelian_group
it sounds possibly like "abelian" is usually used with "group" rather than "field" but that a field contains abelian groups

it sounds like abelian is an adjective used mostly with mathematical groups, generally infinite sets of number-like entities mutated to each other by a strictly commutative operation which the group is said to be diacussed "under" kind of

curious about it still but it's a solid example
so what is the yang mills mass gap? 

hmm it's some kind of esoteric unsolved inference of mainstream quantum physics or something ..
the description of it overlaps math and physics terms freely
so here a "non-abelian field" is likely to refer to a _physical_ field with non-commutative effects 0_0 !