Well, this could go on english.SE imo, but the big users there are pretty ardently against questions from non-native speakers these days. They don't want to clutter their site with lowbrow questions from people not tenured in the humanities. (Okay end of rant, I promise.)
The thing is, articles in English are very context dependent, and there are very few terms that are consistently preceded by one form or another. The definite article the comes before any nouns somehow uniquely defined by the situation:
The force in this particular case...
while the indefinite article a/an precedes nouns that are particular instances where more variety can be imagined:
There is probably an electromagnetic field of some sort worth considering...
Used properly, articles can very well distinguish between unspecified instances of abstract notions and specific, well-defined examples of those notions:
While a manifold is just a topological space locally homeomorphic to R^n, the manifold we will consider is the unique one-dimensional, compact, connected manifold without boundary (i.e. the circle).
There really aren't any better general rules, even for specific things in physics. (Sorry - I've heard English is one of the hardest languages to learn and master, and even as a native speaker I believe it.) That said, on the internet even native speakers (myself included) slip up in more egregious ways than using the wrong article, so I wouldn't worry too much about it.