QFT Basics: What Does "Ad" Mean in Zeidler's Proofs?

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Jimmy Snyder
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I'm reading QFT: Basics in Mathematics and Physics, by Eberhard Zeidler. Once in a while, in his proofs, I see the word (abbreviation?) Ad. For instance on page 375. The author is German and I suppose this imight be common practice in German texts. Does anyone here know what it means?
 
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Jimmy Snyder said:
I'm reading QFT: Basics in Mathematics and Physics, by Eberhard Zeidler. Once in a while, in his proofs, I see the word (abbreviation?) Ad. For instance on page 375. The author is German and I suppose this imight be common practice in German texts. Does anyone here know what it means?
Since you don't give an example and most people will not have that book available, I think many will be able to answer this. Since this is posted under "Quantum Physics", and linear operators are often used there, without any more information I would suspect something line "adjoint" as in "ad T" is the adjoint of the operator T. Was "ad" used with an operator or just as a word on its own?
 
I've seen it used as the prefix for an enumeration of the steps in a proof, but don't know what it stands for. I doubt it's mathematically significant, though I suppose it could also be used to refer back to an enumerated step.
 
my_wan said:
I've seen it used as the prefix for an enumeration of the steps in a proof, but don't know what it stands for.
I'm sorry, I didn't realize that there were some people that don't have a copy of the book. It must stand for some kind of enumeration like case N, case R, etc. That's how it is used on page 375.

The form is like this:

Theorem:
(i) a = b
(ii) b = c
Proof.
Ad (i) ...
Ad (ii) ...
 
It's an abbreviation for "Ad hoc" which means "for this" (case) as you guessed.
 
unusualname said:
It's an abbreviation for "Ad hoc" which means "for this" (case) as you guessed.
Thanks unusualname.