Translation:I wear a sweater under the jacket.
For UK English, its more commonly referred to as "jumper" instead of sweater for Tröja, As far as I know both Jumper and Sweater are the same thing.
Note that "to wear" = "att ha på sig", where "på" should be stressed. This is not really the case with current voice (Nov 19, 2014).
Is it only "har på mig" when referring to yourself and "har på sig" when referring to others? Or can "sig" be used here too?
Jag har på mig
Du har på dig
Han/hon/hen har på sig
Vi har på oss
Ni har på er
De har på sig
It's native to Swedish and comes from Proto-Germanic. Cognates in other Germanic languages include English under, German unter, Dutch onder, and Icelandic undir.
I think it’s originally Germanic, as the meaning shift from originally “between” (cf. Latin inter) to “under” happened in German and English too. In German, the original meaning is preserved as a prefix in some words: unterbrechen (“to under-break”, meaning “to interrupt”), Unternehmen (“under-take”, meaning enterprise) – hey, they are direct translations from their Latin/French/English counterparts!
So directly translated does this not mean "I have on me a sweater under the jacket"? Because it was incorrect for me.
Word by word, that's what it means! But "have on me" is not proper English, right? "Am wearing" sounds so much better :).